Basic Math Examples

$\frac{5^{2} - 3^{3}}{4^{- 2} - 4^{- 1}}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{25 - 3^{3}}{4^{- 2} - 4^{- 1}}$

Step 1.2

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

$\frac{25 - 1 \cdot 27}{4^{- 2} - 4^{- 1}}$

Step 1.3

Multiply $- 1$ by $27$ .

$\frac{25 - 27}{4^{- 2} - 4^{- 1}}$

Step 1.4

Subtract $27$ from $25$ .

$\frac{- 2}{4^{- 2} - 4^{- 1}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{- 2}{\frac{1}{4^{2}} - 4^{- 1}}$

Step 2.2

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

$\frac{- 2}{\frac{1}{16} - 4^{- 1}}$

Step 2.3

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

$\frac{- 2}{\frac{1}{16} - \frac{1}{4}}$

Step 2.4

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{- 2}{\frac{1}{16} - \frac{1}{4} \cdot \frac{4}{4}}$

Step 2.5

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.5.1

Multiply $\frac{1}{4}$ by $\frac{4}{4}$ .

$\frac{- 2}{\frac{1}{16} - \frac{4}{4 \cdot 4}}$

Step 2.5.2

Multiply $4$ by $4$ .

$\frac{- 2}{\frac{1}{16} - \frac{4}{16}}$

Step 2.6

Combine the numerators over the common denominator.

$\frac{- 2}{\frac{1 - 4}{16}}$

Step 2.7

Subtract $4$ from $1$ .

$\frac{- 2}{\frac{- 3}{16}}$

Step 2.8

Move the negative in front of the fraction.

$\frac{- 2}{- \frac{3}{16}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- 2 (- \frac{16}{3})$

Step 4

Multiply $- 2 (- \frac{16}{3})$ .

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Step 4.1

Multiply $- 1$ by $- 2$ .

$2 (\frac{16}{3})$

Step 4.2

Combine $2$ and $\frac{16}{3}$ .

$\frac{2 \cdot 16}{3}$

Step 4.3

Multiply $2$ by $16$ .

$\frac{32}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{32}{3}$

Decimal Form:

$10.\overline{6}$

Mixed Number Form:

$10 \frac{2}{3}$