Simplify (5+5^-2)^0(6^0+6)^-2

${(5 + 5^{- 2})}^{0} {(6^{0} + 6)}^{- 2}$

Simplify each term.

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

${(5 + \frac{1}{5^{2}})}^{0} {(6^{0} + 6)}^{- 2}$

Raise $5$ to the power of $2$ .

${(5 + \frac{1}{25})}^{0} {(6^{0} + 6)}^{- 2}$

To write $5$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

${(5 \cdot \frac{25}{25} + \frac{1}{25})}^{0} {(6^{0} + 6)}^{- 2}$

Combine $5$ and $\frac{25}{25}$ .

${(\frac{5 \cdot 25}{25} + \frac{1}{25})}^{0} {(6^{0} + 6)}^{- 2}$

Combine the numerators over the common denominator.

${(\frac{5 \cdot 25 + 1}{25})}^{0} {(6^{0} + 6)}^{- 2}$

Simplify the numerator.

Multiply $5$ by $25$ .

${(\frac{125 + 1}{25})}^{0} {(6^{0} + 6)}^{- 2}$

Add $125$ and $1$ .

${(\frac{126}{25})}^{0} {(6^{0} + 6)}^{- 2}$

Simplify the expression.

Apply the product rule to $\frac{126}{25}$ .

$\frac{126^{0}}{25^{0}} {(6^{0} + 6)}^{- 2}$

Anything raised to $0$ is $1$ .

$\frac{1}{25^{0}} {(6^{0} + 6)}^{- 2}$

Anything raised to $0$ is $1$ .

$\frac{1}{1} {(6^{0} + 6)}^{- 2}$

Cancel the common factor of $1$ .

Cancel the common factor.

$\frac{1}{1} {(6^{0} + 6)}^{- 2}$

Rewrite the expression.

$1 {(6^{0} + 6)}^{- 2}$

Simplify the expression.

Multiply ${(6^{0} + 6)}^{- 2}$ by $1$ .

${(6^{0} + 6)}^{- 2}$

Anything raised to $0$ is $1$ .

${(1 + 6)}^{- 2}$

Add $1$ and $6$ .

$7^{- 2}$

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:

$0.02040816 \dots$