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?

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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