Write the Fraction in Simplest Form ((b^7)/(4^5))^-3

${(\frac{b^{7}}{4^{5}})}^{- 3}$

Step 1

Raise $4$ to the power of $5$ .

${(\frac{b^{7}}{1024})}^{- 3}$

Step 2

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{1024}{b^{7}})}^{3}$

Step 3

Apply the product rule to $\frac{1024}{b^{7}}$ .

$\frac{1024^{3}}{{(b^{7})}^{3}}$

Step 4

Raise $1024$ to the power of $3$ .

$\frac{1073741824}{{(b^{7})}^{3}}$

Step 5

Multiply the exponents in ${(b^{7})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1073741824}{b^{7 \cdot 3}}$

Multiply $7$ by $3$ .

$\frac{1073741824}{b^{21}}$