Question 1

Which of the following correctly rewrites $$x^{-5}$$ using only positive exponents?

Accepted Answer

$$\frac{1}{x$$^{5}$$}$$

Question 2

Simplify the expression $$3m^{-2} so $$that it contains only positive exponents.

Accepted Answer

$$\frac{3}{m$$^{2}$$}$$

Question 3

Rewrite $$-7a^{-4}b$$^{3}$ using only positive exponents.

Accepted Answer

$$-7\frac{b$$^{3}$$}{a$$^{4}$$}$$

Question 4

Simplify $$\frac{w$$^{-7}$$}{w$$^{9}$$}$$ and write your answer with only positive exponents.

Accepted Answer

$$\frac{1}{w$$^{16}$$}$$

Question 5

Given $$c^{-8}d$$^{3}$$ \cdot c$$^{-5}$$d^{-4}$$, simplify the expression using only positive exponents.

Accepted Answer

$$\frac{1}{c$$^{13}$$d}$$

Question 6

Simplify $$(a^{-5}b$$^{8}$$c^{-12})(a$$^{7}$$b^{-3}c$$^{7}$$)$ and write your answer with only positive exponents.

Accepted Answer

$$a^{2}b$$^{5}$$c^{5}$$

Question 7

A chemist is working with a formula $$p^{-5}(8p$$^{2}$$)$. What is the simplified form with only positive exponents?

Accepted Answer

$$\frac{8}{p$$^{3}$$}$$

Question 8

Simplify $$(5y^{2}$$)^{-3}$ and write your answer with only positive exponents.

Accepted Answer

$$\frac{1}{5$$^{3}$$y^{6}$$}$

Question 9

A biologist is analyzing the growth rate of bacteria modeled by $$6x^{5}y$$^{-4}$$ raised to the power of -2$. What is the simplified form?

Accepted Answer

$$\frac{1}{36x$$^{10}$$y^{8}$$}$

Question 10

Simplify $$\frac{h$$^{2}$$}{h$$^{5}$$}$$ and write your answer with only positive exponents.

Accepted Answer

$$\frac{1}{h$$^{3}$$}$$

Question 11

A physicist is working with the expression $$\frac{m$$^{-2}$$n^{3}$$}{$$m^{5}n$$^{-10}$$}. $$What is the simplified form with only positive exponents?

Accepted Answer

$$\frac{n$$^{13}$$}{m$$^{7}$$}$$

Question 12

Simplify $$\frac{a$$^{2}$$b^{5}c$$^{-4}$$}{a$$^{-3}$$b^{-2}c$$^{7}$$}$$ and write your answer with only positive exponents.

Accepted Answer

$$a^{5}b$$^{7}$$c^{11}$$

Question 13

A medical researcher uses the formula $$\frac{xy$$^{-5}$$z^{3}$$}{$$x^{-4}y$$^{9}$$z^{-2}$$}$ to model a reaction. What is the simplified form?

Accepted Answer

Question 14

Simplify the challenge problem: $$\left(\frac{x$$^{-3}$$y^{-2}$$}{$$x^{-4}y$$^{-4}$$}\right) \cdot \left(\frac{x$$^{-1}$$y^{-7}$$}{$$x^{-2}y$$^{-2}$$}\right)$$ and write your answer with only positive exponents.

Accepted Answer

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

Question 15

A historian is analyzing population growth using the formula $$(4x^{3}y$$^{6}$$)^{-2}$$ + $$(2x^{2}y$$^{4}$$)^{-3}. $$What is the simplified form?

Accepted Answer

$$\frac{1}{16x$$^{6}$$y^{12}$$} + \frac{1}{$$8x^{6}y$$^{12}$$}$$

Question 16

Simplify $$\frac{x$$^{-2}$$y^{-3}$$}{$$x^{-5}y$$^{-4}$$}$$ and write your answer with only positive exponents.

Accepted Answer

$$x^{3}y$$^{1}$

Question 17

A chemist is working with the formula $$\frac{a$$^{-3}$$b^{9}$$}{$$a^{14}$$}$. What is the simplified form with only positive exponents?

Accepted Answer

$$\frac{b$$^{9}$$}{a$$^{17}$$}$$

Question 18

Simplify $$\frac{xy$$^{-4}$$}{x$$^{-6}$$y^{-2}$$}$ and write your answer with only positive exponents.

Accepted Answer

$$x^{7}y$$^{2}$

Negative Exponents: Rules, Simplification, and Practice

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