Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

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

$\frac{5^{- 5 \cdot 4}}{5^{5}}$

Step 1.1.2

Multiply $- 5$ by $4$ .

$\frac{5^{- 20}}{5^{5}}$

Step 1.2

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

$\frac{\frac{1}{5^{20}}}{5^{5}}$

Step 1.3

Raise $5$ to the power of $20$ .

$\frac{\frac{1}{95367431640625}}{5^{5}}$

Step 2

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

$\frac{\frac{1}{95367431640625}}{3125}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{95367431640625} \cdot \frac{1}{3125}$

Step 4

Multiply $\frac{1}{95367431640625} \cdot \frac{1}{3125}$ .

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Step 4.1

Multiply $\frac{1}{95367431640625}$ by $\frac{1}{3125}$ .

$\frac{1}{95367431640625 \cdot 3125}$

Step 4.2

Multiply $95367431640625$ by $3125$ .

$\frac{1}{298023223876953125}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{298023223876953125}$

Decimal Form:

$3.3554432 \cdot 10^{- 18}$