Evaluate (4a)^-3*a^-4

${(4 a)}^{- 3} \cdot a^{- 4}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(4 a)}^{3}} \cdot a^{- 4}$

Step 2

Simplify the denominator.

Apply the product rule to $4 a$ .

$\frac{1}{4^{3} a^{3}} \cdot a^{- 4}$

Raise $4$ to the power of $3$ .

$\frac{1}{64 a^{3}} \cdot a^{- 4}$

Step 3

Cancel the common factor of $a^{- 4}$ .

Factor $a^{- 4}$ out of $64 a^{3}$ .

$\frac{1}{a^{- 4} (64 a^{7})} \cdot a^{- 4}$

Cancel the common factor.

$\frac{1}{a^{- 4} (64 a^{7})} \cdot a^{- 4}$

Rewrite the expression.

$\frac{1}{64 a^{7}}$