Question 1

Multiply and leave your answer in exponent form.
-$\left( 5 x ^ { 3 } y \right) \left( 6 x ^ { 5 } y ^ { 2 } \right)$
A) $30 x ^ { 15 } y ^ { 2 }$
B) $30 x ^ { 8 } y ^ { 3 }$
C) $11 x ^ { 8 } y ^ { 2 }$
D) $30 x ^ { 8 } y ^ { 2 }$

Accepted Answer

When multiplying terms with the same base, you add the exponents. Thus, $5 \times 6 = 30$, $x^3 \times x^5 = x^{3+5} = x^8$, and $y \times y^2 = y^{1+2} = y^3$. Therefore, the correct answer is $30x^8y^3$.

Question 2

Multiply and leave your answer in exponent form. -$$\left( x ^ { 3 } \right) \left( x ^ { 4 } \right)$$ A) $( 2 x ) ^ { 7 }$ B) $x ^ { 7 }$ C)2x⁷ D) $x ^ { 12 }$

Accepted Answer

When multiplying powers with the same base, you add the exponents. Thus, $x^3 \times x^4 = x^{3+4} = x^7$.

Question 3

Multiply and leave your answer in exponent form.
-$$\left( - 3 x ^ { 4 } y ^ { 5 } \right) \left( 8 x y ^ { 5 } \right) \left( - 6 x ^ { 3 } y \right)$$
A) $- 1 x ^ { 12 } y ^ { 25 }$
B) $x ^ { 12 } y ^ { 25 }$
C) $- 1 x ^ { 8 } y ^ { 11 }$
D) $\mathrm { x } ^ { 8 } \mathrm { y } ^ { 11 }$

Accepted Answer

D

Question 4

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero.
-$\frac { s ^ { 5 } t ^ { 15 } } { s ^ { 2 } t }$
A) $s ^ { 3 } t ^ { 13 }$
B) $s ^ { 7 } t ^ { 16 }$
C) $s ^ { 3 } t ^ { 14 }$
D) $s ^ { 3 } t 15$

Accepted Answer

The answer of Divide. Leave your answer in exponent form....

Question 5

Multiply and leave your answer in exponent form. -$\left( 9 ^ { 10 } \right) \left( 9 ^ { 20 } \right)$ A) $81 ^ { 30 }$ B) $9 ^ { 10 }$ C) 9²⁰⁰ D) 9³⁰

Accepted Answer

When multiplying powers with the same base, you add the exponents. Therefore, $9^{10} \times 9^{20} = 9^{10+20} = 9^{30}$. None of the choices directly match this, but choice D, when decoded from its formatting error, likely meant to represent $9^{30}$, making it the correct answer.

Question 6

Multiply and leave your answer in exponent form.
-$$\left( - 2 a ^ { 5 } b \right) \left( - 7 a ^ { 3 } b ^ { 4 } \right) ( 0 )$$
A) $14 a ^ { 8 } b ^ { 5 }$
B) 1
C) $14 a ^ { 5 } b ^ { 4 }$
D) 0

Accepted Answer

When multiplying any number by 0, the result is always 0, regardless of the other factors.

Question 7

Multiply and leave your answer in exponent form.
-$$\left( 2 x ^ { 5 } y \right) \left( - 6 x ^ { 2 } y ^ { 4 } \right)$$
A) $- 12 x ^ { 7 } y ^ { 5 }$
B) $- 12 x ^ { 7 } y ^ { 4 }$
C) $- 12 x ^ { 10 } y ^ { 4 }$
D) $12 x ^ { 7 } y ^ { 4 }$

Accepted Answer

When multiplying terms with exponents, you add the exponents of like bases and multiply the coefficients. Here, $2 \times (-6) = -12$, $x^5 \times x^2 = x^{5+2} = x^7$, and $y \times y^4 = y^{1+4} = y^5$, resulting in $-12x^7y^5$.

Question 8

Multiply and leave your answer in exponent form.
-$( 7 x ) \left( 8 x ^ { 5 } \right) \left( x ^ { 7 } \right)$
A) $56 \mathrm { x } ^ { 12 }$
B) $15 x ^ { 12 }$
C) $56 x ^ { 13 }$
D) $16 \mathrm { x } ^ { 13 }$

Accepted Answer

When multiplying terms with the same base, you add the exponents. Here, $7 \times 8 = 56$ and $x^1 \times x^5 \times x^7 = x^{1+5+7} = x^{13}$, so the answer is $56x^{13}$.

Question 9

Multiply and leave your answer in exponent form.
-$$\left( - 5 x ^ { 4 } \right) \left( - 9 x ^ { 6 } \right)$$
A) $- 45 x 10$
B) $- 45 x ^ { 24 }$
C) $45 x ^ { 10}$
D) $45 x ^ { 24 }$

Accepted Answer

When multiplying powers with the same base, you add the exponents. Thus, $(-5x^4)(-9x^6) = 45x^{4+6} = 45x^{10}$.

Question 10

Write in simplest exponent form.
-9 ·9 ·9 ·9 · x · x · x 
A) $9 ^ { 5 } x ^ { 3 }$
B) $9 ^ { 4 } x ^ { 3 }$
C) $6 x ^ { 3 }$
D) $9 x ^ { 7 }$

Accepted Answer

The expression simplifies to $9^4 x^3$ because there are four instances of 9 being multiplied together and three instances of x, so the correct exponent form is $9^4 x^3$.

Question 11

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero.
-$\frac { z ^ { 13 } } { z ^ { 12 } }$
A) $\mathrm { z }$
B) $\frac { 1 } { z }$
C) $\mathrm { z } ^ { 25 }$
D) $z ^ { 13 } - z ^ { 12 }$

Accepted Answer

When dividing powers with the same base, subtract the exponents: $z^{13-12} = z^1 = z$.

Question 12

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero.
-$\frac { 12 m ^ { 3 } n ^ { 10 } } { 4 m ^ { 2 } n ^ { 7 } }$
A) $3 n ^ { 3 }$
B) $3 m n ^ { 3 }$
C) $12 \mathrm { mn } ^ { 3 }$
D) $3 m ^ { 5 } n$

Accepted Answer

To divide the given expression, divide the coefficients and subtract the exponents of like bases: $12/4 = 3$, $m^{3-2} = m^1$, and $n^{10-7} = n^3$, resulting in $3m^1n^3$.

Question 13

Multiply and leave your answer in exponent form. -$\left( 5 ^ { 9 } \right) \left( 5 ^ { 8 } \right)$ A) 5⁷² B) 25⁷² C) 25¹⁷ D) 5¹⁷

Accepted Answer

When multiplying powers with the same base, you add the exponents: $5^9 \times 5^8 = 5^{9+8} = 5^{17}$.

Question 14

Multiply and leave your answer in exponent form.
-$$\left( - 8 x ^ { 6 } y \right) \left( - 8 x ^ { 3 } y ^ { 5 } \right)$$
A) $- 64 x ^ { 9 } y ^ { 5 }$
B) $- 16 x ^ { 9 } y ^ { 5 }$
C) $64 x ^ { 9 } y ^ { 6 }$
D) $64 x ^ { 18 } y ^ { 5 }$

Accepted Answer

When multiplying powers with the same base, you add the exponents. Thus, $(-8) \times (-8) = 64$, $x^6 \times x^3 = x^{6+3} = x^9$, and $y \times y^5 = y^{1+5} = y^6$. Therefore, the product is $64 x^9 y^6$.

Question 15

Write in simplest exponent form.
-4 ·4 ·4 ·4 ·4 ·4 · x · x 
A) $4 ^ { 6 } x ^ { 2 }$
B) $6 ^ { 4 } x ^ { 2 }$
C) $24 x ^ { 2 }$
D) $4^5 x ^ { 2 }$

Accepted Answer

The expression simplifies to $4^6 x^2$ because there are six 4's multiplied together and two x's multiplied together.

Question 16

Multiply and leave your answer in exponent form.
-$$\left( \mathrm { z } ^ { 10 } \right) \left( \mathrm { z } ^ { 14 } \right)$$
A) $z ^ { 4 }$
B) $z ^ { 140 }$
C)2$z ^ { 24 }$
D) $z ^ { 24 }$

Accepted Answer

When multiplying powers with the same base, you add the exponents. Thus, $z^{10} \times z^{14} = z^{10+14} = z^{24}$.

Question 17

Write in simplest exponent form.
-x · x · x · x 
A) $4 x$
B) $4 ^ { x }$
C) 4
D) $x ^ { 4 }$

Accepted Answer

When you multiply a number by itself, you add the exponents. Since x is being multiplied by itself 4 times, it is written as $x^4$.

Question 18

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero.
-$\frac { 15 x ^ { 7 } y ^ { 5 } } { 75 x ^ { 4 } y ^ { 9 } }$
A) $5 x ^ { 3 } y ^ { 4 }$
B) $\frac { x ^ { 11 } } { 5 y ^ { 14 } }$
C) $\frac { 5 x ^ { 3 } } { y ^ { 4 } }$
D) $\frac { x ^ { 3 } } { 5 y ^ { 4 } }$

Accepted Answer

First, simplify the coefficients: $15/75 = 1/5$. Then, use the laws of exponents for the variables: $x^{7-4} = x^3$ and $y^{5-9} = y^{-4}$. Combine these results to get $\frac{1}{5}x^3y^{-4}$, which simplifies to $\frac{x^3}{5y^4}$.

Question 19

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero.
-$\frac { 3 ^ { 16 } } { 3 ^ { 14 } }$
A) $- 3 ^ { 2 }$
B) $\frac { 1 } { 3 ^ { 2 } }$
C) $\frac { 1 } { - 3 ^ { 2 } }$
D) $3 ^ { 2 }$

Accepted Answer

When dividing powers with the same base, subtract the exponents: $3^{16} / 3^{14} = 3^{16-14} = 3^2$.

Question 20

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero.
-$\frac { a ^ { 9 } } { a }$
A) $a ^ { 9 } - a$
B) $a ^ { 8 }$
C) $a 10$
D) 9

Accepted Answer

When dividing powers with the same base, subtract the exponents: $a^9 / a = a^{9-1} = a^8$.

Quiz 5: Exponents and Polynomials

Multiply and leave your answer in exponent form. - $\left( 5 x ^ { 3 } y \right) \left( 6 x ^ { 5 } y ^ { 2 } \right)$

Multiply and leave your answer in exponent form. - $\left( x ^ { 3 } \right) \left( x ^ { 4 } \right)$

Multiply and leave your answer in exponent form. - $\left( - 3 x ^ { 4 } y ^ { 5 } \right) \left( 8 x y ^ { 5 } \right) \left( - 6 x ^ { 3 } y \right)$

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. - $\frac { s ^ { 5 } t ^ { 15 } } { s ^ { 2 } t }$

Multiply and leave your answer in exponent form. - $\left( 9 ^ { 10 } \right) \left( 9 ^ { 20 } \right)$

Multiply and leave your answer in exponent form. - $\left( - 2 a ^ { 5 } b \right) \left( - 7 a ^ { 3 } b ^ { 4 } \right) ( 0 )$

Multiply and leave your answer in exponent form. - $\left( 2 x ^ { 5 } y \right) \left( - 6 x ^ { 2 } y ^ { 4 } \right)$

Multiply and leave your answer in exponent form. - $( 7 x ) \left( 8 x ^ { 5 } \right) \left( x ^ { 7 } \right)$

Multiply and leave your answer in exponent form. - $\left( - 5 x ^ { 4 } \right) \left( - 9 x ^ { 6 } \right)$

Write in simplest exponent form. -9 ·9 ·9 ·9 · x · x · x

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. - $\frac { z ^ { 13 } } { z ^ { 12 } }$

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. - $\frac { 12 m ^ { 3 } n ^ { 10 } } { 4 m ^ { 2 } n ^ { 7 } }$

Multiply and leave your answer in exponent form. - $\left( 5 ^ { 9 } \right) \left( 5 ^ { 8 } \right)$

Multiply and leave your answer in exponent form. - $\left( - 8 x ^ { 6 } y \right) \left( - 8 x ^ { 3 } y ^ { 5 } \right)$

Write in simplest exponent form. -4 ·4 ·4 ·4 ·4 ·4 · x · x

Multiply and leave your answer in exponent form. - $\left( \mathrm { z } ^ { 10 } \right) \left( \mathrm { z } ^ { 14 } \right)$

Write in simplest exponent form. -x · x · x · x

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. - $\frac { 15 x ^ { 7 } y ^ { 5 } } { 75 x ^ { 4 } y ^ { 9 } }$

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. - $\frac { 3 ^ { 16 } } { 3 ^ { 14 } }$

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. - $\frac { a ^ { 9 } } { a }$

Quiz 5: Exponents and Polynomials

Multiply and leave your answer in exponent form. - (5x3y) (6x5y2) \left( 5 x ^ { 3 } y \right) \left( 6 x ^ { 5 } y ^ { 2 } \right) (5x3y) (6x5y2)

Multiply and leave your answer in exponent form. - (x3) (x4) \left( x ^ { 3 } \right) \left( x ^ { 4 } \right) (x3) (x4)

Multiply and leave your answer in exponent form. - (−3x4y5) (8xy5) (−6x3y) \left( - 3 x ^ { 4 } y ^ { 5 } \right) \left( 8 x y ^ { 5 } \right) \left( - 6 x ^ { 3 } y \right) (−3x4y5) (8xy5) (−6x3y)

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. - s5t15s2t\frac { s ^ { 5 } t ^ { 15 } } { s ^ { 2 } t }s2ts5t15​

Multiply and leave your answer in exponent form. - (910) (920) \left( 9 ^ { 10 } \right) \left( 9 ^ { 20 } \right) (910) (920)

Multiply and leave your answer in exponent form. - (−2a5b) (−7a3b4) (0) \left( - 2 a ^ { 5 } b \right) \left( - 7 a ^ { 3 } b ^ { 4 } \right) ( 0 ) (−2a5b) (−7a3b4) (0)

Multiply and leave your answer in exponent form. - (2x5y) (−6x2y4) \left( 2 x ^ { 5 } y \right) \left( - 6 x ^ { 2 } y ^ { 4 } \right) (2x5y) (−6x2y4)

Multiply and leave your answer in exponent form. - (7x) (8x5) (x7) ( 7 x ) \left( 8 x ^ { 5 } \right) \left( x ^ { 7 } \right) (7x) (8x5) (x7)

Multiply and leave your answer in exponent form. - (−5x4) (−9x6) \left( - 5 x ^ { 4 } \right) \left( - 9 x ^ { 6 } \right) (−5x4) (−9x6)