6.5 Divide Monomials

Before you get started, take this readiness quiz.

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

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

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

Simplify: ⓐ $\frac{x^{15}}{x^{10}}$ ⓑ $\frac{6^{14}}{6^{5}} .$

Simplify: ⓐ $\frac{y^{43}}{y^{37}}$ ⓑ $\frac{10^{15}}{10^{7}} .$

Simplify: ⓐ $\frac{x^{18}}{x^{22}}$ ⓑ $\frac{12^{15}}{12^{30}} .$

Simplify: ⓐ $\frac{m^{7}}{m^{15}}$ ⓑ $\frac{9^{8}}{9^{19}} .$

Simplify: ⓐ $\frac{b^{19}}{b^{11}}$ ⓑ $\frac{z^{5}}{z^{11}} .$

Simplify: ⓐ $\frac{p^{9}}{p^{17}}$ ⓑ $\frac{w^{13}}{w^{9}} .$

Simplify: ⓐ $9^{0}$ ⓑ $n^{0} .$

Simplify: ⓐ $15^{0}$ ⓑ $m^{0} .$

Simplify: ⓐ $k^{0}$ ⓑ $29^{0} .$

Simplify: ⓐ $\left(5 b\right)^{0}$ ⓑ $\left(−4 a^{2} b\right)^{0} .$

Simplify: ⓐ $\left(11 z\right)^{0}$ ⓑ $\left(−11 p q^{3}\right)^{0} .$

Simplify: ⓐ $\left(−6 d\right)^{0}$ ⓑ $\left(−8 m^{2} n^{3}\right)^{0} .$

Simplify: ⓐ $\left(\frac{5}{8}\right)^{2}$ ⓑ $\left(\frac{p}{10}\right)^{4}$ ⓒ $\left(\frac{m}{n}\right)^{7} .$

Simplify: ⓐ $\left(\frac{1}{3}\right)^{3}$ ⓑ $\left(\frac{−2}{q}\right)^{3}$ ⓒ $\left(\frac{w}{x}\right)^{4} .$

Simplify: $\frac{\left(y^{4}\right)^{2}}{y^{6}} .$

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

Simplify: $\frac{\left(k^{2}\right)^{6}}{k^{7}} .$

Simplify: $\frac{b^{12}}{\left(b^{2}\right)^{6}} .$

Simplify: $\frac{n^{12}}{\left(n^{3}\right)^{4}} .$

Simplify: $\frac{x^{15}}{\left(x^{3}\right)^{5}} .$

Simplify: $\left(\frac{y^{9}}{y^{4}}\right)^{2} .$

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

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

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

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

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

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

Simplify: $\left(\frac{7 x^{3}}{9 y}\right)^{2} .$

Simplify: $\left(\frac{3 x^{4}}{7 y}\right)^{2} .$

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

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

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

Simplify: $\frac{\left(10 p^{3}\right)^{2}}{\left(5 p\right)^{3} \left(2 p^{5}\right)^{4}} .$

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

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

Find the quotient: $56 x^{7} \div 8 x^{3} .$

Find the quotient: $42 y^{9} \div 6 y^{3} .$

Find the quotient: $48 z^{8} \div 8 z^{2} .$

Find the quotient: $\frac{45 a^{2} b^{3}}{−5 a b^{5}} .$

Find the quotient: $\frac{−72 a^{7} b^{3}}{8 a^{12} b^{4}} .$

Find the quotient: $\frac{−63 c^{8} d^{3}}{7 c^{12} d^{2}} .$

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

Find the quotient: $\frac{\left(6 a^{4} b^{5}\right) \left(4 a^{2} b^{5}\right)}{12 a^{5} b^{8}} .$

Find the quotient: $\frac{\left(−12 x^{6} y^{9}\right) \left(−4 x^{5} y^{8}\right)}{−12 x^{10} y^{12}} .$

Simplify.

ⓐ $\frac{y^{20}}{y^{10}}$ ⓑ $\frac{7^{16}}{7^{2}}$

Simplify.

ⓐ $\frac{u^{24}}{u^{3}}$ ⓑ $\frac{9^{15}}{9^{5}}$

Simplify.

ⓐ $\frac{t^{10}}{t^{40}}$ ⓑ $\frac{8^{3}}{8^{5}}$

Simplify.

ⓐ $\frac{x}{x^{7}}$ ⓑ $\frac{10}{10^{3}}$

Simplify.

ⓐ $13^{0}$ ⓑ $k^{0}$

Simplify.

ⓐ $− 15^{0}$ ⓑ $− \left(15^{0}\right)$

Simplify.

ⓐ $\left(6 y\right)^{0}$ ⓑ $6 y^{0}$

Simplify.

ⓐ $7 y^{0}$$\left(17 y\right)^{0}$ ⓑ $\left(−93 c^{7} d^{15}\right)^{0}$

Simplify.

ⓐ $15 r^{0} - 22 s^{0}$ ⓑ $\left(15 r\right)^{0} - \left(22 s\right)^{0}$

Simplify.

ⓐ $\left(\frac{2}{5}\right)^{2}$ ⓑ $\left(\frac{x}{3}\right)^{4}$ ⓒ $\left(\frac{a}{b}\right)^{5}$

Simplify.

ⓐ $\left(\frac{x}{2 y}\right)^{3}$ ⓑ $\left(\frac{10}{3 q}\right)^{4}$

Simplify.

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

Simplify.

$\frac{\left(x^{4}\right)^{5}}{x^{15}}$

Simplify.

$\frac{v^{20}}{\left(v^{4}\right)^{5}}$

Simplify.

$\frac{n^{8}}{\left(n^{6}\right)^{4}}$

Simplify.

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

Simplify.

$\left(\frac{m^{4}}{m^{7}}\right)^{4}$

Simplify.

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

Simplify.

$\left(\frac{y^{4}}{z^{10}}\right)^{5}$

Simplify.

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

Simplify.

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

Simplify.

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

Simplify.

$\frac{\left(q^{3}\right)^{6} \left(q^{2}\right)^{3}}{\left(q^{4}\right)^{8}}$

Simplify.

$\frac{\left(−2 k^{3}\right)^{2} \left(6 k^{2}\right)^{4}}{\left(9 k^{4}\right)^{2}}$

Simplify.

$\frac{\left(−10 n^{2}\right)^{3} \left(4 n^{5}\right)^{2}}{\left(2 n^{8}\right)^{2}}$

Divide the monomials.

$63 v^{10} \div \textrm{ } 9 v^{2}$

Divide the monomials.

$−72 u^{12} \div \textrm{ } 1 2 u^{4}$

Divide the monomials.

$\frac{54 x^{9} y^{3}}{−18 x^{6} y^{15}}$

Divide the monomials.

$\frac{20 m^{8} n^{4}}{30 m^{5} n^{9}}$

Divide the monomials.

$\frac{45 x^{5} y^{9}}{−60 x^{8} y^{6}}$

Divide the monomials.

$\frac{65 a^{10} b^{8} c^{5}}{42 a^{7} b^{6} c^{8}}$

Divide the monomials.

$\frac{\left(−18 p^{4} q^{7}\right) \left(−6 p^{3} q^{8}\right)}{−36 p^{12} q^{10}}$

Divide the monomials.

$\frac{\left(4 u^{2} v^{5}\right) \left(15 u^{3} v\right)}{\left(12 u^{3} v\right) \left(u^{4} v\right)}$

Mixed Practice

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

Mixed Practice

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

Mixed Practice

ⓐ $\frac{z^{6}}{z^{5}}$ ⓑ $\frac{z^{5}}{z^{6}}$

Mixed Practice

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

Mixed Practice

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

Mixed Practice

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

Mixed Practice

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

Memory One gigabyte is approximately $10^{9}$ bytes. One terabyte is approximately $10^{12}$ bytes. How many gigabytes are in one terabyte?

Maurice simplifies the quotient $\frac{d^{7}}{d}$ by writing $\frac{\cancel{d}^{7}}{\cancel{d}} = 7$. What is wrong with his reasoning?

Robert thinks $x^{0}$ simplifies to 0. What would you say to convince Robert he is wrong?