Basic Math Examples

$\frac{5^{8}}{{(5^{- 4})}^{- 3}}$

Step 1

Move ${(5^{- 4})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$5^{8} {(5^{- 4})}^{3}$

Step 2

Raise $5$ to the power of $8$ .

$390625 {(5^{- 4})}^{3}$

Step 3

Multiply the exponents in ${(5^{- 4})}^{3}$ .

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Step 3.1

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

$390625 \cdot 5^{- 4 \cdot 3}$

Step 3.2

Multiply $- 4$ by $3$ .

$390625 \cdot 5^{- 12}$

Step 4

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

$390625 \cdot \frac{1}{5^{12}}$

Step 5

Raise $5$ to the power of $12$ .

$390625 \cdot \frac{1}{244140625}$

Step 6

Cancel the common factor of $390625$ .

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Step 6.1

Factor $390625$ out of $244140625$ .

$390625 \cdot \frac{1}{390625 (625)}$

Step 6.2

Cancel the common factor.

$390625 \cdot \frac{1}{390625 \cdot 625}$

Step 6.3

Rewrite the expression.

$\frac{1}{625}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{625}$

Decimal Form:

$0.0016$