Simplify (3^4)^-4

${(3^{4})}^{- 4}$

Step 1

Multiply the exponents in ${(3^{4})}^{- 4}$ .

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

$3^{4 \cdot - 4}$

Multiply $4$ by $- 4$ .

$3^{- 16}$

Step 2

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

$\frac{1}{3^{16}}$

Step 3

Raise $3$ to the power of $16$ .

$\frac{1}{43046721}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{43046721}$

Decimal Form:

$2.32305731 \cdot 10^{- 8}$