Quotient Rule for Exponents

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Show your work for each problem.

1.
Simplify $\frac{7^9}{7^3}$ .
1. a) $7^6$
2. b) $7^3$
3. c) $7^{12}$
4. d) $1^6$
2.
$\frac{x^{11}}{x^4} = x^{\square}$ . What number goes in the box?
3.
Simplify $\frac{2^8}{2^5}$ and evaluate it.
4.
Which expression equals $\frac{a^{10}}{a^2}$ (with $a \neq 0$ )?
1. a) $a^{12}$
2. b) $a^5$
3. c) $a^{20}$
4. d) $a^8$
5.
Evaluate $\frac{10^9}{10^6}$ .
6.
Simplify $\frac{y^7}{y^2}$ by cancelling factors.
7.
Ana simplified $\frac{x^{12}}{x^3}$ and got $x^4$ . What did she do wrong?
1. a)She divided the bases
2. b)She subtracted the exponents in the wrong order
3. c)She divided the exponents instead of subtracting them
4. d)Nothing, $x^4$ is correct
8.
$\frac{15x^8}{3x^5} = \square\, x^3$ . What number goes in the box?
9.
Simplify $\frac{20m^9}{5m^4}$ .
10.
Simplify $\frac{24a^7b^4}{8a^3b}$ .
1. a) $16a^4b^3$
2. b) $3a^4b^3$
3. c) $3a^{10}b^5$
4. d) $3a^4b^4$
11.
Evaluate $\frac{3^{10}}{3^7}$ .
12.
Simplify $\frac{18p^6q^5}{6p^2q^3}$ .
13.
Simplify $\frac{4^3 \cdot 4^5}{4^6}$ and evaluate it.
14.
Which expression is NOT equal to $x^6$ (with $x \neq 0$ )?
1. a) $\frac{x^2 \cdot x^7}{x^3}$
2. b) $\frac{x^9}{x^3}$
3. c) $\frac{x^{12}}{x^2}$
4. d) $\frac{x^{10}}{x^4}$
15.
$\frac{x^{\square}}{x^4} = x^9$ . What number goes in the box?
16.
Simplify $\frac{6x^5 \cdot 3x^4}{9x^7}$ .
17.
Simplify $\frac{5a^3 \cdot 4a^6}{10a^2 \cdot a^4}$ .
18.
A hard drive holds $2^{40}$ bytes. One film takes $2^{32}$ bytes. How many films fit on the drive?