Question 1

In the expression $- 2 ^ { 15 }$ , what is the base and the exponent?

Accepted Answer

2, 15

Question 2

Simplify the expression. $$\left( 2 y ^ { 2 } \right) ^ { 4 }$$
A) $16 y ^ { 6 }$
B) $16 y ^ { 8 }$
C) $2 y ^ { 8 }$
D) $16 y ^ { 4 }$
E) $2 y ^ { 2 }$

Accepted Answer

To simplify the expression, we need to raise $2y^2$ to the fourth power. This can be done by multiplying the exponent of $2y^2$ by 4, which gives us $2^4 \cdot (y^2)^4$ or $16y^8$. Therefore, the answer is $\boxed{	extbf{(B)}\ 16y^8}$.

Question 3

Simplify the following expression. Do not use parentheses or negative exponents. $- ( - 9 ) ^ { - 2 }$
A)81
B)-81
C)-18
D) $\frac { 1 } { 81 }$
E) $- \frac { 1 } { 81 }$

Accepted Answer

E

Question 4

Simplify the following expression. Assume that $$y \neq 0$$ . $$\frac { 8 y ^ { 4 } \cdot y ^ { 6 } \cdot y ^ { 6 } } { 2 \left( y ^ { 4 } \right) ^ { 3 } }$$
A) $4 y ^ { 137 }$
B) $4 y ^ { 4 }$
C) $6 y ^ { 4 }$
D) $4 y ^ { 9 }$
E) $8 y ^ { 4 }$

Accepted Answer

When simplifying the expression, use the properties of exponents. The numerator simplifies to $8y^{16}$ (since $y^4 \cdot y^6 \cdot y^6 = y^{4+6+6} = y^{16}$). The denominator simplifies to $2y^{12}$ (since $(y^4)^3 = y^{4\cdot3} = y^{12}$). Dividing the numerator by the denominator gives $4y^4$.

Question 5

Simplify the expression. $$\left( 2 y ^ { 6 } c ^ { 9 } \right) ^ { 2 }$$
A) $4 y ^ { 12 } c ^ { 18 }$
B) $2 y ^ { 8 } c ^ { 11 }$
C) $4 y ^ { 6 } c ^ { 9 }$
D) $4 y ^ { 8 } c ^ { 11 }$
E) $2 y ^ { 12 } c ^ { 18 }$

Accepted Answer

When simplifying the expression $\left( 2 y ^ { 6 } c ^ { 9 } \right) ^ { 2 }$, you apply the power of a power rule, which states that $(a^m)^n = a^{mn}$. Therefore, each component of the expression is squared: $2^2 = 4$, $y^{6 \cdot 2} = y^{12}$, and $c^{9 \cdot 2} = c^{18}$, resulting in $4 y ^ { 12 } c ^ { 18 }$.

Question 6

Write the expression without using exponents. $19.3 c ^ { 0 }$
A)1
B)19.3
C)-19.3
D)0

Accepted Answer

Any number raised to the power of 0 equals 1, so $c^0$ is equal to 1. Therefore, $19.3 c ^ { 0 }$ simplifies to 19.3 multiplied by 1, which equals 19.3.

Question 7

Simplify the following expression. $$x ^ { 4 } \cdot x ^ { 2 } \left( x ^ { 4 } \cdot x ^ { 2 } \right) \left( x ^ { 4 } \cdot x ^ { 2 } \right)$$
A) $x ^ { 6 }$
B) $x ^ { 8 }$
C) $6 x ^ { 16 }$
D) $x ^ { 16 }$
E) $x ^ { 18 }$

Accepted Answer

The expression simplifies to $x^{4+2+4+2+4+2} = x^{18}$.

Question 8

$- 8 t ( - 8 t ) = ( - 8 t ) ^ { 2 }$

Accepted Answer

The left-hand side of the equation can be simplified by multiplying -8t with -8t, resulting in 64t^2.

Therefore:

-8t(-8t) = 64t^2

And the right-hand side of the equation is (-8t)^2 which is also 64t^2.

Therefore, the equation simplifies to:

64t^2 = 64t^2

Which is true, making the statement true as well.

Question 9

Write the expression without using exponents. ( -0.4797 ) $0$
A)0
B)-0.4797
C)-0.735
D)1

Accepted Answer

Any number raised to the power of 0 is equal to 1, regardless of the base number.

Question 10

Write the following expression as an expression involving only one base and one exponent. $$\left( 4 s ^ { 3 } s ^ { 4 } s ^ { 3 } \right) ^ { 2 }$$
A) $16 s ^ { 10 }$
B) $16 s ^ { 8 }$
C) $4 s ^ { 20 }$
D) $16 s ^ { 12 }$
E) $16 s ^ { 20 }$

Accepted Answer

First, simplify inside the parentheses: $4s^3 \cdot s^4 \cdot s^3 = 4s^{3+4+3} = 4s^{10}$. Then, apply the exponent outside the parentheses: $(4s^{10})^2 = 4^2s^{10\cdot2} = 16s^{20}$.

Question 11

Simplify. $$\left( 15 ^ { 5 } \right) ^ { 3 }$$
A) $15 ^ { 15 }$
B) $15 ^ { 5 }$
C) $15 ^ { 3 }$
D) $15 ^ { 8 }$

Accepted Answer

When raising a power to another power, you multiply the exponents. So, $(15^5)^3 = 15^{5*3} = 15^{15}$.

Question 12

Simplify by writing the expression without using parentheses. $$\left( \frac { a ^ { 3 } a ^ { 2 } } { a ^ { 6 } } \right) ^ { 6 }$$
A) $\frac { 1 } { a }$
B) $\frac { 1 } { a ^ { 6 } }$
C) $\frac { 1 } { a ^ { 6 } }$.
D) $\frac { 1 } { 6 a ^ { 6 } }$
E) $a ^ { 6 }$

Accepted Answer

Using exponent rules, we have:

$$\left( \frac { a ^ { 3 } a ^ { 2 } } { a ^ { 6 } } \right) ^ { 6 } = \frac{a^{3+2}}{a^{6\cdot 6}} = \frac{a^5}{a^{36}} = a^{5-36} = a^{-31} = \frac{1}{a^{31}} = \boxed{\frac{1}{a^6}}$$

Question 13

Simplify the expression. $$\left( s ^ { 5 } s ^ { 4 } \right) ^ { 2 }$$
A) $s ^ { 28 }$
B) $s ^ { 22 }$
C) $s ^ { 18 }$
D) $s ^ { 8 }$
E) $s ^ { 11 }$

Accepted Answer

When multiplying powers with the same base, you add the exponents. So, $s^5 \cdot s^4 = s^{5+4} = s^9$. Then, raising $s^9$ to the power of 2, you multiply the exponents: $(s^9)^2 = s^{9 \cdot 2} = s^{18}$.

Question 14

In the expression -9², what is the base?

Accepted Answer

The answer of In the expression -9², what is the...

Question 15

Simplify the following expression. $$\left( \frac { 2 a ^ { 2 } \cdot a ^ { 3 } \cdot a ^ { 6 } } { 3 a ^ { 3 } \cdot a ^ { 2 } } \right) ^ { 3 }$$
A) $\frac { 8 a ^ { 18 } } { 27 }$
B) $\frac { 8 a ^ { 24 } } { 27 }$
C) $\frac { 2 a ^ { 11 } } { 3 a ^ { 5 } }$
D) $\frac { 2 a ^ { 18 } } { 3 }$
E) $\frac { 8 a ^ { 18 } } { 3 a ^ { 5 } }$

Accepted Answer

First, simplify the expression inside the parentheses by adding the exponents of $a$ in the numerator and subtracting the exponents of $a$ in the denominator: $2a^{2+3+6}/3a^{3+2} = 2a^{11}/3a^{5}$. Then, simplify the fraction: $2/3 \cdot a^{11-5} = 2/3 \cdot a^{6}$. Raising this to the power of 3 gives $(2/3)^3 \cdot a^{6 \cdot 3} = 8/27 \cdot a^{18}$, which matches option A.

Question 16

In the expression $- 5 ^ { 3 }$ , what is the exponent?

Accepted Answer

The answer of In the expression \(- 5 ^ {...

Question 17

Write the expression without using exponents. $$( - 17 ) ^ { 0 }$$
A)0
B)-17
C)17
D)1

Accepted Answer

Any number (except 0) raised to the power of 0 is always equal to 1.

Question 18

Simplify the following expression. $$x ^ { 6 } \cdot x ^ { 2 }$$
A) $x ^ { 4 }$
B) $x ^ { 12 }$
C) $2 x ^ { 36 }$
D) $x ^ { 36 }$
E) $x ^ { 8 }$

Accepted Answer

When multiplying two exponents with the same base, we add the exponents. 
So, $x ^ { 6 } \cdot x ^ { 2 } = x ^ { 6+2} = x ^ 8$.

Question 19

Write the following expression without using a negative exponent. $( - 32 ) ^ { - 1 }$
A)1
B)32
C) $- \frac { 1 } { 32 }$
D)-32
E) $\frac { 1 } { 32 }$

Accepted Answer

To write the expression without a negative exponent, you take the reciprocal of the base. Thus, $(-32)^{-1}$ becomes $-\frac{1}{32}$.

Question 20

Select the expression that completes the formula below. $$( x y ) ^ { k }$$
A) $x ^ { k } y ^ { k }$
B) $x ^ { m + k }$
C) $x ^ { m k }$
D) $\frac { x ^ { k } } { y ^ { k } }$
E)None of these

Accepted Answer

When raising a product to a power, we can distribute the exponent to each factor. Therefore, $$(xy)^k = x^ky^k.$$

Quiz 5: Exponents and Polynomials

In the expression $- 2 ^ { 15 }$ , what is the base and the exponent?

Simplify the expression. $\left( 2 y ^ { 2 } \right) ^ { 4 }$

Simplify the following expression. Do not use parentheses or negative exponents. $- ( - 9 ) ^ { - 2 }$

Simplify the following expression. Assume that $y \neq 0$ . $\frac { 8 y ^ { 4 } \cdot y ^ { 6 } \cdot y ^ { 6 } } { 2 \left( y ^ { 4 } \right) ^ { 3 } }$

Simplify the expression. $\left( 2 y ^ { 6 } c ^ { 9 } \right) ^ { 2 }$

Write the expression without using exponents. $19.3 c ^ { 0 }$

Simplify the following expression. $x ^ { 4 } \cdot x ^ { 2 } \left( x ^ { 4 } \cdot x ^ { 2 } \right) \left( x ^ { 4 } \cdot x ^ { 2 } \right)$

$- 8 t ( - 8 t ) = ( - 8 t ) ^ { 2 }$

Write the expression without using exponents. ( -0.4797 ) $0$

Write the following expression as an expression involving only one base and one exponent. $\left( 4 s ^ { 3 } s ^ { 4 } s ^ { 3 } \right) ^ { 2 }$

Simplify. $\left( 15 ^ { 5 } \right) ^ { 3 }$

Simplify by writing the expression without using parentheses. $\left( \frac { a ^ { 3 } a ^ { 2 } } { a ^ { 6 } } \right) ^ { 6 }$

Simplify the expression. $\left( s ^ { 5 } s ^ { 4 } \right) ^ { 2 }$

In the expression -9², what is the base?

Simplify the following expression. $\left( \frac { 2 a ^ { 2 } \cdot a ^ { 3 } \cdot a ^ { 6 } } { 3 a ^ { 3 } \cdot a ^ { 2 } } \right) ^ { 3 }$

In the expression $- 5 ^ { 3 }$ , what is the exponent?

Write the expression without using exponents. $( - 17 ) ^ { 0 }$

Simplify the following expression. $x ^ { 6 } \cdot x ^ { 2 }$

Write the following expression without using a negative exponent. $( - 32 ) ^ { - 1 }$

Select the expression that completes the formula below. $( x y ) ^ { k }$

Quiz 5: Exponents and Polynomials

In the expression −215- 2 ^ { 15 }−215 , what is the base and the exponent?

Simplify the expression. (2y2) 4\left( 2 y ^ { 2 } \right) ^ { 4 }(2y2) 4

Simplify the following expression. Do not use parentheses or negative exponents. −(−9) −2- ( - 9 ) ^ { - 2 }−(−9) −2

Simplify the following expression. Assume that y≠0y \neq 0y=0 . 8y4⋅y6⋅y62(y4) 3\frac { 8 y ^ { 4 } \cdot y ^ { 6 } \cdot y ^ { 6 } } { 2 \left( y ^ { 4 } \right) ^ { 3 } }2(y4) 38y4⋅y6⋅y6​

Simplify the expression. (2y6c9) 2\left( 2 y ^ { 6 } c ^ { 9 } \right) ^ { 2 }(2y6c9) 2

Write the expression without using exponents. 19.3c019.3 c ^ { 0 }19.3c0

Simplify the following expression. x4⋅x2(x4⋅x2) (x4⋅x2) x ^ { 4 } \cdot x ^ { 2 } \left( x ^ { 4 } \cdot x ^ { 2 } \right) \left( x ^ { 4 } \cdot x ^ { 2 } \right) x4⋅x2(x4⋅x2) (x4⋅x2)

−8t(−8t)=(−8t)2- 8 t ( - 8 t ) = ( - 8 t ) ^ { 2 }−8t(−8t)=(−8t)2

Write the expression without using exponents. ( -0.4797 ) 000

Write the following expression as an expression involving only one base and one exponent. (4s3s4s3) 2\left( 4 s ^ { 3 } s ^ { 4 } s ^ { 3 } \right) ^ { 2 }(4s3s4s3) 2

Simplify. (155) 3\left( 15 ^ { 5 } \right) ^ { 3 }(155) 3

Simplify by writing the expression without using parentheses. (a3a2a6) 6\left( \frac { a ^ { 3 } a ^ { 2 } } { a ^ { 6 } } \right) ^ { 6 }(a6a3a2​) 6

Simplify the expression. (s5s4) 2\left( s ^ { 5 } s ^ { 4 } \right) ^ { 2 }(s5s4) 2

In the expression -92, what is the base?

Simplify the following expression. (2a2⋅a3⋅a63a3⋅a2) 3\left( \frac { 2 a ^ { 2 } \cdot a ^ { 3 } \cdot a ^ { 6 } } { 3 a ^ { 3 } \cdot a ^ { 2 } } \right) ^ { 3 }(3a3⋅a22a2⋅a3⋅a6​) 3

In the expression −53- 5 ^ { 3 }−53 , what is the exponent?

Write the expression without using exponents. (−17) 0( - 17 ) ^ { 0 }(−17) 0

Simplify the following expression. x6⋅x2x ^ { 6 } \cdot x ^ { 2 }x6⋅x2

Write the following expression without using a negative exponent. (−32) −1( - 32 ) ^ { - 1 }(−32) −1

Select the expression that completes the formula below. (xy) k( x y ) ^ { k }(xy) k

In the expression $- 2 ^ { 15 }$ , what is the base and the exponent?

Simplify the expression. $\left( 2 y ^ { 2 } \right) ^ { 4 }$

Simplify the following expression. Do not use parentheses or negative exponents. $- ( - 9 ) ^ { - 2 }$

Simplify the following expression. Assume that $y \neq 0$ . $\frac { 8 y ^ { 4 } \cdot y ^ { 6 } \cdot y ^ { 6 } } { 2 \left( y ^ { 4 } \right) ^ { 3 } }$

Simplify the expression. $\left( 2 y ^ { 6 } c ^ { 9 } \right) ^ { 2 }$

Write the expression without using exponents. $19.3 c ^ { 0 }$

Simplify the following expression. $x ^ { 4 } \cdot x ^ { 2 } \left( x ^ { 4 } \cdot x ^ { 2 } \right) \left( x ^ { 4 } \cdot x ^ { 2 } \right)$

$- 8 t ( - 8 t ) = ( - 8 t ) ^ { 2 }$

Write the expression without using exponents. ( -0.4797 ) $0$

Write the following expression as an expression involving only one base and one exponent. $\left( 4 s ^ { 3 } s ^ { 4 } s ^ { 3 } \right) ^ { 2 }$

Simplify. $\left( 15 ^ { 5 } \right) ^ { 3 }$

Simplify by writing the expression without using parentheses. $\left( \frac { a ^ { 3 } a ^ { 2 } } { a ^ { 6 } } \right) ^ { 6 }$

Simplify the expression. $\left( s ^ { 5 } s ^ { 4 } \right) ^ { 2 }$

In the expression -9², what is the base?

Simplify the following expression. $\left( \frac { 2 a ^ { 2 } \cdot a ^ { 3 } \cdot a ^ { 6 } } { 3 a ^ { 3 } \cdot a ^ { 2 } } \right) ^ { 3 }$

In the expression $- 5 ^ { 3 }$ , what is the exponent?

Write the expression without using exponents. $( - 17 ) ^ { 0 }$

Simplify the following expression. $x ^ { 6 } \cdot x ^ { 2 }$

Write the following expression without using a negative exponent. $( - 32 ) ^ { - 1 }$

Select the expression that completes the formula below. $( x y ) ^ { k }$