Question 1

Simplify.
-$\left(\frac{\mathrm{x}^{5}}{\mathrm{y}^{5} \mathrm{z}^{4}}\right)^{4}$

Accepted Answer

When raising a power to a power in an expression, you multiply the exponents. Thus, $\left(\frac{x^5}{y^5z^4}\right)^4 = \frac{x^{5*4}}{y^{5*4}z^{4*4}} = \frac{x^{20}}{y^{20}z^{16}}$.

Question 2

Simplify.
-$\left(\frac{b^{5}}{2}\right)^{-2}$

Accepted Answer

When simplifying $\left(\frac{b^{5}}{2}\right)^{-2}$, you apply the negative exponent rule, which flips the fraction and squares both the numerator and denominator. This results in $\frac{4}{b^{10}}$.

Question 3

Simplify.
-$\left(\frac{x y^{3}}{w^{4} z}\right)^{-5}$

Accepted Answer

When simplifying $\left(\frac{x y^{3}}{w^{4} z}\right)^{-5}$, you flip the fraction due to the negative exponent and raise each term to the power of -5, resulting in $\frac{w^{20} z^{5}}{x^{5} y^{15}}$.

Question 4

Write the number in scientific notation.
-6646

Accepted Answer

To write 6646 in scientific notation, you move the decimal point 3 places to the left, which gives $6.646 \times 10^{3}$.

Question 5

Write the number in scientific notation.
-58

Accepted Answer

To write 58 in scientific notation, we express it as $5.8 \times 10^{1}$, which means 5.8 times 10 to the power of 1, correctly representing the number 58.

Question 6

Write the number in scientific notation.
-146.447

Accepted Answer

The number 146.447 can be expressed in scientific notation as $1.46447 \times 10^{2}$ because the decimal point is moved two places to the left.

Question 7

Write the number in scientific notation.
-890,000

Accepted Answer

The number 890,000 can be written in scientific notation as $8.9 \times 10^{5}$ because the decimal point is moved 5 places to the left to convert it to a number between 1 and 10.

Question 8

Write the number in scientific notation.
-$14,000,000$

Accepted Answer

$14,000,000$ in scientific notation is $1.4 \times 10^{7}$, because you move the decimal 7 places to the left to get from 14,000,000 to 1.4.

Question 9

Write the number in scientific notation.
-0.000603

Accepted Answer

To convert 0.000603 into scientific notation, we move the decimal point 4 places to the right, making it $6.03 \times 10^{-4}$.

Question 10

Write the number in scientific notation.
-0.000097614

Accepted Answer

To convert 0.000097614 into scientific notation, we move the decimal point 5 places to the right, making it $9.7614 \times 10^{-5}$.

Question 11

Write the number in scientific notation.
-0.000007064

Accepted Answer

The number 0.000007064 can be expressed in scientific notation as $7.064 \times 10^{-6}$ because the decimal point is moved 6 places to the right to get the number 7.064.

Question 12

Write the number in scientific notation.
-0.00000028905

Accepted Answer

To convert 0.00000028905 to scientific notation, we move the decimal point 7 places to the right, making it $2.8905 \times 10^{-7}$.

Question 13

Write the number in scientific notation.
-0.0000000833018

Accepted Answer

To convert 0.0000000833018 into scientific notation, we move the decimal point 8 places to the right, making it $8.33018 \times 10^{-8}$.

Question 14

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation.
-The population of a small country is $3,302,000$.

Accepted Answer

The population of $3,302,000$ can be written in scientific notation as $3.302 \times 10^{6}$, moving the decimal point 6 places to the left.

Question 15

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation.
-A company produces 919,000 small appliances in one year.

Accepted Answer

The correct scientific notation for 919,000 is $9.19 \times 10^{5}$, because you move the decimal point 5 places to the left to get 9.19 from 919,000.

Question 16

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation.
-The speed of light is $1.86 \times 10^{5}$ miles per hour.

Accepted Answer

The scientific notation $1.86 \times 10^{5}$ represents the number 186,000 when written without exponents.

Question 17

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation.
-A computer can do one calculation in $1.4 \times 10^{-7}$ seconds.

Accepted Answer

The scientific notation $1.4 \times 10^{-7}$ seconds means the decimal point is moved 7 places to the left, making it 0.00000014 seconds.

Question 18

Convert to decimal notation.
-$1.52 \times 10^{4}$

Accepted Answer

$1.52 \times 10^{4}$ means that the decimal point in 1.52 is moved 4 places to the right, resulting in 15,200.

Question 19

Convert to decimal notation.
-$6.072 \times 10^{5}$

Accepted Answer

The expression $6.072 \times 10^{5}$ means moving the decimal point 5 places to the right, resulting in 607,200.

Question 20

Convert to decimal notation.
-$3.0599 \times 10^{4}$

Accepted Answer

To convert $3.0599 \times 10^{4}$ to decimal notation, move the decimal point 4 places to the right, resulting in 30,599.

Quiz 4: Polynomials: Operations

Simplify. - $\left(\frac{\mathrm{x}^{5}}{\mathrm{y}^{5} \mathrm{z}^{4}}\right) ^{4}$

Simplify. - $\left(\frac{b^{5}}{2}\right) ^{-2}$

Simplify. - $\left(\frac{x y^{3}}{w^{4} z}\right) ^{-5}$

Write the number in scientific notation. -6646

Write the number in scientific notation. -58

Write the number in scientific notation. -146.447

Write the number in scientific notation. -890,000

Write the number in scientific notation. - $14,000,000$

Write the number in scientific notation. -0.000603

Write the number in scientific notation. -0.000097614

Write the number in scientific notation. -0.000007064

Write the number in scientific notation. -0.00000028905

Write the number in scientific notation. -0.0000000833018

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -The population of a small country is $3,302,000$ .

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -A company produces 919,000 small appliances in one year.

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -The speed of light is $1.86 \times 10^{5}$ miles per hour.

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -A computer can do one calculation in $1.4 \times 10^{-7}$ seconds.

Convert to decimal notation. - $1.52 \times 10^{4}$

Convert to decimal notation. - $6.072 \times 10^{5}$

Convert to decimal notation. - $3.0599 \times 10^{4}$

Quiz 4: Polynomials: Operations

Simplify. - (x5y5z4) 4\left(\frac{\mathrm{x}^{5}}{\mathrm{y}^{5} \mathrm{z}^{4}}\right) ^{4}(y5z4x5​) 4

Simplify. - (b52) −2\left(\frac{b^{5}}{2}\right) ^{-2}(2b5​) −2

Simplify. - (xy3w4z) −5\left(\frac{x y^{3}}{w^{4} z}\right) ^{-5}(w4zxy3​) −5