Basic Math Examples

$\frac{{(- 5)}^{2} - 4^{2} + {(120^{10})}^{0}}{3^{- 2} + 1}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{25 - 4^{2} + {(120^{10})}^{0}}{3^{- 2} + 1}$

Step 1.2

Raise $4$ to the power of $2$ .

$\frac{25 - 1 \cdot 16 + {(120^{10})}^{0}}{3^{- 2} + 1}$

Step 1.3

Multiply $- 1$ by $16$ .

$\frac{25 - 16 + {(120^{10})}^{0}}{3^{- 2} + 1}$

Step 1.4

Multiply the exponents in ${(120^{10})}^{0}$ .

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Step 1.4.1

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

$\frac{25 - 16 + 120^{10 \cdot 0}}{3^{- 2} + 1}$

Step 1.4.2

Multiply $10$ by $0$ .

$\frac{25 - 16 + 120^{0}}{3^{- 2} + 1}$

Step 1.5

Anything raised to $0$ is $1$ .

$\frac{25 - 16 + 1}{3^{- 2} + 1}$

Step 1.6

Subtract $16$ from $25$ .

$\frac{9 + 1}{3^{- 2} + 1}$

Step 1.7

Add $9$ and $1$ .

$\frac{10}{3^{- 2} + 1}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{10}{\frac{1}{3^{2}} + 1}$

Step 2.2

Raise $3$ to the power of $2$ .

$\frac{10}{\frac{1}{9} + 1}$

Step 2.3

Write $1$ as a fraction with a common denominator.

$\frac{10}{\frac{1}{9} + \frac{9}{9}}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{10}{\frac{1 + 9}{9}}$

Step 2.5

Add $1$ and $9$ .

$\frac{10}{\frac{10}{9}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$10 (\frac{9}{10})$

Step 4

Cancel the common factor of $10$ .

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Step 4.1

Cancel the common factor.

$10 (\frac{9}{10})$

Step 4.2

Rewrite the expression.

$9$