Question 1

Which of the following expressions is equivalent to $$x^{-4}$$ with only positive exponents?

Accepted Answer

$$\dfrac{1}{x^4$}$$

Question 2

Simplify the expression $$\dfrac{2$$^{-3}$$ \cdot 5^2$}{10$$^{-2}$$}$$ and write your answer with positive exponents only.

Accepted Answer

$$\dfrac{5^4$}{2^3$}$$

Question 3

Which of the following is the correct scientific notation for the number 0.000072?

Accepted Answer

$$7.2 	imes 10$$^{-5}$$

Question 4

Convert $$3.45 	imes 10^7$ to decimal notation.

Accepted Answer

$$34,500,000$$

Question 5

Simplify the expression $$\$$left(2x^{-3}$$y^2$$\$$right)^{-2}$ and write your answer with positive exponents only.

Accepted Answer

$$\dfrac{x^6$}{4y^4$}$$

Question 6

Which of the following is the decimal notation for $$5.6 	imes 10$$^{-4}$$?

Accepted Answer

$$0.00056$$

Question 7

Write $$0.00000039 in $$scientific notation.

Accepted Answer

$$3.9 	imes 10$$^{-7}$$

Question 8

Simplify the expression $$\dfrac{6x$$^{-2}$$y^3$$}{$$3x^4y$$^{-1}$$}$$ and write your answer with positive exponents only.

Accepted Answer

Question 9

A hospital stores $$2.5 	imes 10^6$ milligrams of a medication. How many grams is this? (Recall: 1 gram = 1000 milligrams.)

Accepted Answer

$$2.5 	imes 10^3$ grams

Question 10

Simplify $$\left(4 	imes 10^3$ight) 	imes \left(2 	imes 10$$^{-5}$$ight)$$ and write your answer in scientific notation.

Accepted Answer

$$8 	imes 10$$^{-2}$$

Question 11

Divide $$6.0 	imes 10^8$ by 3.0$$ 	imes $$10^4$$ and write your answer in scientific notation.

Accepted Answer

$$2.0 	imes 10^4$

Question 12

Simplify $$\left(5 	imes 10^2$\$$right)^3$$ and write your answer in scientific notation.

Accepted Answer

$$1.25 	imes 10^8$

Question 13

A city has a population of $$3.2 	imes 10^6$ people. If each person is allocated 1.5$$ 	imes $$10^3$$ liters of water per year, how many liters of water does the city use per year? Express your answer in scientific notation.

Accepted Answer

$$4.8 	imes 10^9$

Question 14

Which of the following is equivalent to $$\dfrac{a$$^{-2}$$b^3$$}{$$c^{-4}$$}$ with only positive exponents?

Accepted Answer

$$\dfrac{b^3$c^4$$}{$$a^2$$}$

Question 15

Write $$987,000,000 in $$scientific notation.

Accepted Answer

$$9.87 	imes 10^8$

Question 16

Simplify $$\dfrac{(2x^3$y^{-2})^2$}{4x$$^{-1}$$y^4$$}$ and write your answer with positive exponents only.

Accepted Answer

Question 17

A scientist measures a bacteria population as $$4.2 	imes 10^5$ cells. If the population doubles every hour, what will the population be after 3 hours? Express your answer in scientific notation.

Accepted Answer

$$3.36 	imes 10^6$

Question 18

Which of the following is the correct simplification of $$\left(\dfrac{3x$$^{-2}$$}{y^3$}\$$right)^{-1}$$ with positive exponents only?

Accepted Answer

$$\dfrac{x^2$}{3y^3$}$$

Question 19

The mass of the Earth is approximately $$5.97 	imes 10$$^{24}$$ kilograms. Write this number in decimal notation.

Accepted Answer

$$5,970,000,000,000,000,000,000,000$$

Question 20

A chemical reaction produces $$1.2 	imes 10$$^{-3}$$ moles of product per second. How many moles are produced in 2.5$$ 	imes $$10^4$$ seconds? Express your answer in scientific notation.

Accepted Answer

$$3.0 	imes 10^1$

Negative Exponents and Scientific Notation: Study Guide

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