Question 1

Simplify the expression $$\displaystyle \frac{y^7$}{y^5$}$$ using the quotient rule for exponents.

Accepted Answer

$$y^{2}$$

Question 2

What is the value of $$\displaystyle \frac{m^6$}{m^6$}$$ for any nonzero $$m$$?

Accepted Answer

$$1$$

Question 3

Which rule allows you to simplify $$\displaystyle \frac{a^m}{a^n} as$$ $$a^{m-n}$$?

Accepted Answer

Quotient Rule

Question 4

Evaluate $$a^0$$ for any nonzero $$a.$$

Accepted Answer

$$1$$

Question 5

Simplify $$\displaystyle \frac{y$$^{27}$$}{y^9$}.$$

Accepted Answer

$$y^{18}$$

Question 6

Simplify $$\displaystyle \frac{64}{16}.$$

Accepted Answer

$$4$$

Question 7

Evaluate $$(-4t)^0$$ for $$t 
eq 0.$$

Accepted Answer

$$1$$

Question 8

Simplify $$\displaystyle \frac{12b$$^{11}$$}{4b^7$}.$$

Accepted Answer

$$3b^{4}$$

Question 9

Simplify $$\displaystyle \frac{9x^2$y^8$$}{$$3xy^2$$}$.

Accepted Answer

$$3x y^6$

Question 10

Simplify $$\displaystyle \frac{30x^5$y^3z^3$}{-15x^2$y^3z$$}$.

Accepted Answer

$$-2x^3z^2$

Question 11

Simplify $$\displaystyle \frac{(x^2$)^4$$}{$$(x^3)^3$}.$$

Accepted Answer

$$x^{-1}$$

Question 12

Which of the following is equivalent to $$(3^4)^2$?

Accepted Answer

$$3^8$$

Question 13

Simplify $$\displaystyle \left(\frac{3}{4}\$$right)^2$$.

Accepted Answer

$$\frac{9}{16}$$

Question 14

Simplify $$\displaystyle \frac{2^2$}{2^5$}.$$

Accepted Answer

$$2^{-3}$$

Question 15

Which rule is used to simplify $$\displaystyle (a \cdot b)^m$$?

Accepted Answer

Power of a Product Rule

Question 16

Simplify $$\displaystyle (4z^2$)^3$.

Accepted Answer

$$4^3z^6$

Question 17

Simplify $$\displaystyle (x^2$z^5)^4$.

Accepted Answer

$$x^8z$$^{20}$

Question 18

Simplify $$\displaystyle \left(\frac{y^4$}{5}\$$right)^3$$.

Accepted Answer

$$\frac{y$$^{12}$$}{125}$$

Question 19

Simplify $$\displaystyle \frac{2$$^{-1}$$ \cdot 2^4$}{2^3$}.$$

Accepted Answer

$$2^0$$

Question 20

Which of the following is the correct simplification of $$a^{-n}$$?

Accepted Answer

$$\frac{1}{a^n}$$

Mastering the Quotient Rule for Exponents

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