3.8 Exponents

If possible, use the product rule to simplify the following:

1. $21^{9} \times 21^{15}$
2. $5^{9} \times 8^{4}$

Use the product rule to simplify $a^{4} \times a^{10}$.

Use the quotient rule to simplify $\frac{5^{19}}{5^{11}}$.

Use the exponent distributive rule to expand $\left(6 \times 13\right)^{7}$.

Use the exponent distributive rule to expand $\left(c \times d\right)^{10}$.

Use the exponent distributive rule to expand the following:

1. $\left(\frac{4}{9}\right)^{6}$
2. $\left(\frac{3}{b}\right)^{11}$

Expand the following:

1. $\left(6^{7}\right)^{3}$
2. $\left(b^{12}\right)^{4}$

Convert the following to expressions with no negative exponent:

1. $3^{4} \times 5^{- 8}$
2. $a^{- 9} \times b^{5}$
3. $\frac{7}{c^{- 2}}$

Use negative exponents to rewrite the following expressions with no denominator:

1. $\frac{7^{3}}{13^{9}}$
2. $\frac{c^{4}}{d^{8}}$

Simplify the following:

1. $\left(\frac{4^{2} \times 7}{9^{3}}\right)^{5}$
2. $\left(\frac{5 a^{4}}{b^{9}}\right)^{6}$