Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

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

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

Step 3

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5$ by $25$ .

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

Step 5.2

Add $125$ and $1$ .

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

Step 6

Simplify the expression.

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Step 6.1

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

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

Step 6.2

Anything raised to $0$ is $1$ .

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

Step 6.3

Anything raised to $0$ is $1$ .

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

Step 7

Cancel the common factor of $1$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

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

Step 8

Simplify the expression.

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Step 8.1

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

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

Step 8.2

Anything raised to $0$ is $1$ .

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

Step 8.3

Add $1$ and $6$ .

$7^{- 2}$

Step 9

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

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

Step 10

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

$\frac{1}{49}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{49}$

Decimal Form:

$0.02040816 \dots$