Evaluate ((7^4)/(7^2))^-1

${(\frac{7^{4}}{7^{2}})}^{- 1}$

Cancel the common factor of $7^{4}$ and $7^{2}$ .

Factor $7^{2}$ out of $7^{4}$ .

${(\frac{7^{2} \cdot 7^{2}}{7^{2}})}^{- 1}$

Cancel the common factors.

Multiply by $1$ .

${(\frac{7^{2} \cdot 7^{2}}{7^{2} \cdot 1})}^{- 1}$

Cancel the common factor.

${(\frac{7^{2} \cdot 7^{2}}{7^{2} \cdot 1})}^{- 1}$

Rewrite the expression.

${(\frac{7^{2}}{1})}^{- 1}$

Divide $7^{2}$ by $1$ .

${(7^{2})}^{- 1}$

Multiply the exponents in ${(7^{2})}^{- 1}$ .

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

$7^{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$7^{- 2}$

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

$\frac{1}{7^{2}}$

Raise $7$ to the power of $2$ .

$\frac{1}{49}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{49}$

Decimal Form:

$0.02040816 \dots$