10.4 Divide Monomials

Before you get started, take this readiness quiz.

Simplify: $\frac{8}{24} .$
If you missed the problem, review the reference.

Simplify: $\left(2 m^{3}\right)^{5} .$
If you missed the problem, review the reference.

Simplify: $\frac{12 x^{}}{12 y} .$
If you missed the problem, review the reference.

Simplify:

1. ⓐ $\frac{x^{12}}{x^{9}}$
2. ⓑ $\frac{7^{14}}{7^{5}}$

Simplify:

1. ⓐ $\frac{y^{23}}{y^{17}}$
2. ⓑ $\frac{8^{15}}{8^{7}}$

Simplify:

1. ⓐ $\frac{x^{8}}{x^{15}}$
2. ⓑ $\frac{12^{11}}{12^{21}}$

Simplify:

1. ⓐ $\frac{m^{17}}{m^{26}}$
2. ⓑ $\frac{7^{8}}{7^{14}}$

Simplify:

1. ⓐ $\frac{b^{19}}{b^{11}}$
2. ⓑ $\frac{z^{5}}{z^{11}}$

Simplify:

1. ⓐ $\frac{p^{9}}{p^{17}}$
2. ⓑ $\frac{w^{13}}{w^{9}}$

Simplify:

1. ⓐ $12^{0}$
2. ⓑ $y^{0}$

Simplify:

1. ⓐ $17^{0}$
2. ⓑ $m^{0}$

Simplify:

1. ⓐ $k^{0}$
2. ⓑ $29^{0}$

Simplify: $\left(7 z\right)^{0} .$

Simplify: $\left(−4 y\right)^{0} .$

Simplify: $\left(\frac{2}{3} x\right)^{0} .$

Simplify:

1. ⓐ $\left(−3 x^{2} y\right)^{0}$
2. ⓑ $−3 x^{2} y^{0}$

Simplify:

1. ⓐ $\left(7 x^{2} y\right)^{0}$
2. ⓑ $7 x^{2} y^{0}$

Simplify:

1. ⓐ $−23 x^{2} y^{0}$
2. ⓑ $\left(−23 x^{2} y\right)^{0}$

Simplify:

1. ⓐ $\left(\frac{7}{9}\right)^{2}$
2. ⓑ $\left(\frac{y}{8}\right)^{3}$
3. ⓒ $\left(\frac{p}{q}\right)^{6}$

Simplify:

1. ⓐ $\left(\frac{1}{8}\right)^{2}$
2. ⓑ $\left(\frac{−5}{m}\right)^{3}$
3. ⓒ $\left(\frac{r}{s}\right)^{4}$

Simplify: $\frac{\left(x^{2}\right)^{3}}{x^{5}} .$

Simplify: $\frac{\left(a^{4}\right)^{5}}{a^{9}} .$

Simplify: $\frac{\left(b^{5}\right)^{6}}{b^{11}} .$

Simplify: $\frac{m^{8}}{\left(m^{2}\right)^{4}} .$

Simplify: $\frac{k^{11}}{\left(k^{3}\right)^{3}} .$

Simplify: $\frac{d^{23}}{\left(d^{4}\right)^{6}} .$

Simplify: $\left(\frac{x^{7}}{x^{3}}\right)^{2} .$

Simplify: $\left(\frac{f^{14}}{f^{8}}\right)^{2} .$

Simplify: $\left(\frac{b^{6}}{b^{11}}\right)^{2} .$

Simplify: $\left(\frac{p^{2}}{q^{5}}\right)^{3} .$

Simplify: $\left(\frac{m^{3}}{n^{8}}\right)^{5} .$

Simplify: $\left(\frac{t^{10}}{u^{7}}\right)^{2} .$

Simplify: $\left(\frac{2 x^{3}}{3 y}\right)^{4} .$

Simplify: $\left(\frac{5 b}{9 c^{3}}\right)^{2} .$

Simplify: $\left(\frac{4 p^{4}}{7 q^{5}}\right)^{3} .$

Simplify: $\frac{\left(y^{2}\right)^{3} \left(y^{2}\right)^{4}}{\left(y^{5}\right)^{4}} .$

Simplify: $\frac{\left(y^{4}\right)^{4} \left(y^{3}\right)^{5}}{\left(y^{7}\right)^{6}} .$

Simplify: $\frac{\left(3 x^{4}\right)^{2} \left(x^{3}\right)^{4}}{\left(x^{5}\right)^{3}} .$

Find the quotient: $56 x^{5} \div 7 x^{2} .$

Find the quotient: $63 x^{8} \div 9 x^{4} .$

Find the quotient: $96 y^{11} \div 6 y^{8} .$

Find the quotient: $\frac{42 x^{2} y^{3}}{−7 x y^{5}} .$

Find the quotient: $\frac{−84 x^{8} y^{3}}{7 x^{10} y^{2}} .$

Find the quotient: $\frac{−72 a^{4} b^{5}}{−8 a^{9} b^{5}} .$

Find the quotient: $\frac{24 a^{5} b^{3}}{48 a b^{4}} .$

Find the quotient: $\frac{16 a^{7} b^{6}}{24 a b^{8}} .$

Find the quotient: $\frac{27 p^{4} q^{7}}{−45 p^{12} q^{}} .$

Find the quotient: $\frac{14 x^{7} y^{12}}{21 x^{11} y^{6}} .$

Find the quotient: $\frac{28 x^{5} y^{14}}{49 x^{9} y^{12}} .$

Find the quotient: $\frac{30 m^{5} n^{11}}{48 m^{10} n^{14}} .$

Find the quotient: $\frac{\left(3 x^{3} y^{2}\right) \left(10 x^{2} y^{3}\right)}{6 x^{4} y^{5}} .$

Find the quotient: $\frac{\left(3 x^{4} y^{5}\right) \left(8 x^{2} y^{5}\right)}{12 x^{5} y^{8}} .$

Find the quotient: $\frac{\left(−6 a^{6} b^{9}\right) \left(−8 a^{5} b^{8}\right)}{−12 a^{10} b^{12}} .$

Simplify.

$\frac{4^{8}}{4^{2}}$

Simplify.

$\frac{x^{12}}{x^{3}}$

Simplify.

$\frac{r^{5}}{r}$

Simplify.

$\frac{y^{4}}{y^{20}}$

Simplify.

$\frac{10^{3}}{10^{15}}$

Simplify.

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

Simplify.

$5^{0}$

Simplify.

$a^{0}$

Simplify.

$- 7^{0}$

Simplify.

1. ⓐ $\left(10 p\right)^{0}$
2. ⓑ $10 p^{0}$

Simplify.

1. ⓐ $\left(−27 x^{5} y\right)^{0}$
2. ⓑ $−27 x^{5} y^{0}$

Simplify.

1. ⓐ $15^{0}$
2. ⓑ $15^{1}$

Simplify.

$2 \cdot x^{0} + 5 \cdot y^{0}$

Simplify.

$\left(\frac{3}{2}\right)^{5}$

Simplify.

$\left(\frac{m}{6}\right)^{3}$

Simplify.

$\left(\frac{x}{y}\right)^{10}$

Simplify.

$\left(\frac{a}{3 b}\right)^{2}$

Simplify.

$\frac{\left(x^{2}\right)^{4}}{x^{5}}$

Simplify.

$\frac{\left(u^{3}\right)^{4}}{u^{10}}$

Simplify.

$\frac{y^{8}}{\left(y^{5}\right)^{2}}$

Simplify.

$\frac{r^{5}}{r^{4} \cdot r}$

Simplify.

$\left(\frac{x^{2}}{x^{8}}\right)^{3}$

Simplify.

$\left(\frac{a^{4} \cdot a^{6}}{a^{3}}\right)^{2}$

Simplify.

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

Simplify.

$\frac{\left(x^{3}\right)^{6}}{\left(x^{4}\right)^{7}}$

Simplify.

$\left(\frac{2 r^{3}}{5 s}\right)^{4}$

Simplify.

$\left(\frac{3 y^{2} \cdot y^{5}}{y^{15} \cdot y^{8}}\right)^{0}$

Simplify.

$\frac{\left(r^{2}\right)^{5} \left(r^{4}\right)^{2}}{\left(r^{3}\right)^{7}}$

Simplify.

$\frac{\left(3 x^{4}\right)^{3} \left(2 x^{3}\right)^{2}}{\left(6 x^{5}\right)^{2}}$

Divide the monomials.

$48 b^{8} \div 6 b^{2}$

Divide the monomials.

$36 x^{3} \div \left(−2 x^{9}\right)$

Divide the monomials.

$\frac{18 x^{3}}{9 x^{2}}$

Divide the monomials.

$\frac{−35 x^{7}}{−42 x^{13}}$

Divide the monomials.

$\frac{18 r^{5} s}{3 r^{3} s^{9}}$

Divide the monomials.

$\frac{8 m n^{10}}{64 m n^{4}}$

Divide the monomials.

$\frac{−12 x^{4} y^{9}}{15 x^{6} y^{3}}$

Divide the monomials.

$\frac{64 x^{5} y^{9} z^{7}}{48 x^{7} y^{12} z^{6}}$

Divide the monomials.

$\frac{\left(6 m^{2} n\right) \left(5 m^{4} n^{3}\right)}{3 m^{10} n^{2}}$

Divide the monomials.

$\frac{\left(4 u^{5} v^{4}\right) \left(15 u^{8} v\right)}{\left(12 u^{3} v\right) \left(u^{6} v\right)}$

1. ⓐ $15 n^{10} + 3 n^{10}$
2. ⓑ $15 n^{10} - 3 n^{10}$
3. ⓒ $15 n^{10} \cdot 3 n^{10}$
4. ⓓ $15 n^{10} \div 3 n^{10}$

1. ⓐ $q^{5} \cdot q^{3}$
2. ⓑ $\left(q^{5}\right)^{3}$

1. ⓐ $\frac{z^{6}}{z^{5}}$
2. ⓑ $\frac{z^{5}}{z^{6}}$

$\left(4 y\right) \left(12 y^{7}\right) \div 8 y^{2}$

$\frac{32 c^{11}}{4 c^{5}} + \frac{42 c^{9}}{6 c^{3}}$

$\frac{48 x^{6}}{6 x^{4}} - \frac{35 x^{9}}{7 x^{7}}$

$\frac{56 y^{4} z^{5}}{7 y^{3} z^{3}} - \frac{45 y^{2} z^{2}}{5 y}$

Memory One megabyte is approximately $10^{6}$ bytes. One terabyte is approximately $10^{12}$ bytes. How many megabytes are in one terabyte?

Mai simplifies the quotient $\frac{y^{3}}{y}$ by writing $\frac{\cancel{y}^{3}}{\cancel{y}} = 3 .$ What is wrong with her reasoning?

Roxie thinks $n^{0}$ simplifies to $0 .$ What would you say to convince Roxie she is wrong?