Q: Which of the following is the correct method to simplify $$ (a \times 10^b)^n $$?

$$ a^n \times 10$$^{b \times n}$$ $$

Q: Which of the following is the correct answer to $$ (7.5 \times 10$$^{-3}$$)^5$$ \div \sqrt[4]{8.6 \times $$10^{21}$$} $?

$$ 2.4 \times 10$$^{-11}$$ \div 1.7 \times 10^5$ = 1.4 \times 10$$^{-16}$$ $$

Question 1

When raising a number in scientific notation to a power, which of the following steps is correct?

Accepted Answer

Raise the coefficient to the power and multiply the exponent by the power.

Question 2

What is the result of $$ (3.0 	imes 10$$^{-2}$$)^3$$ $ in scientific notation?

Accepted Answer

$$ 2.7 	imes 10$$^{-6}$$ $$

Question 3

Which of the following correctly expresses $$ \sqrt[3]{6.0 	imes 10^9$}  in $$scientific notation?

Accepted Answer

$$ 1.8 	imes 10^3$ $$

Question 4

A laboratory sample has a mass of $$ 7.5 	imes 10$$^{-3}$$ $$ grams. If this mass is raised to the 5th power, what is the result in scientific notation?

Accepted Answer

$$ 2.4 	imes 10$$^{-11}$$ $$

Question 5

Which of the following is the correct method to simplify $$ (a 	imes 10^b)^n $$?

Accepted Answer

$$ a^n 	imes 10$$^{b 	imes n}$$ $$

Question 6

If you take the 4th root of $$ 8.6 	imes 10$$^{21}$$ $$, what is the result in scientific notation?

Accepted Answer

$$ 1.7 	imes 10^5$ $$

Question 7

Which of the following best describes the process for taking the nth root of a number in scientific notation?

Accepted Answer

Take the nth root of the coefficient and divide the exponent by n.

Question 8

A medication is prepared at a concentration of $$ 6.0 	imes 10^9$ $$ molecules per mL. If a pharmacist needs the cube root of this concentration, what is the correct value?

Accepted Answer

$$ 1.8 	imes 10^3$ $$

Question 9

Which of the following is the correct answer to $$ (7.5 	imes 10$$^{-3}$$)^5$$ \div \sqrt[4]{8.6 	imes $$10^{21}$$} $?

Accepted Answer

$$ 2.4 	imes 10$$^{-11}$$ \div 1.7 	imes 10^5$ = 1.4 	imes 10$$^{-16}$$ $$

Question 10

If $$ x = 3.0 	imes 10$$^{-2}$$ $$, what is $$ x^3$ $$?

Accepted Answer

$$ 2.7 	imes 10$$^{-6}$$ $$

Question 11

A scientist needs to express $$ (5.0 	imes 10^4$)^2$$ $ in scientific notation. What is the correct answer?

Accepted Answer

$$ 2.5 	imes 10^9$ $$

Question 12

Which of the following is the correct simplification for $$ \sqrt[3]{2.7 	imes 10$$^{-6}$$} $$?

Accepted Answer

$$ 1.4 	imes 10$$^{-3}$$ $$

Question 13

If you have $$ (4.0 	imes 10^5$)^2$$ $, what is the result?

Accepted Answer

$$ 1.6 	imes 10$$^{10}$$ $$

Question 14

A solution contains $$ 2.0 	imes 10$$^{-8}$$ $$ mol/L. What is the square root of this concentration?

Accepted Answer

$$ 1.4 	imes 10$$^{-4}$$ $$

Question 15

Which of the following is the correct result for $$ (1.0 	imes 10^3$)^{1/2}$$ $?

Accepted Answer

$$ 1.0 	imes 10$$^{1.5}$$ $$

Question 16

A nurse needs to dilute a solution from $$ 8.0 	imes 10^6$  to$$ $$ 2.0 	imes 10^3$ . By $$what factor should the solution be diluted?

Accepted Answer

$$ 4.0 	imes 10^3$ $$

Scientific Notation: Powers and Roots

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