Basic Math Examples

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

Step 1

Multiply ${(\frac{1}{5})}^{2}$ by ${(\frac{1}{5})}^{- 6}$ by adding the exponents.

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Step 1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.2

Subtract $6$ from $2$ .

$\frac{{(\frac{1}{5})}^{- 4}}{{(\frac{1}{5})}^{2}}$

Step 2

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

$\frac{1}{{(\frac{1}{5})}^{2} {(\frac{1}{5})}^{4}}$

Step 3

Multiply ${(\frac{1}{5})}^{2}$ by ${(\frac{1}{5})}^{4}$ by adding the exponents.

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Step 3.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{{(\frac{1}{5})}^{2 + 4}}$

Step 3.2

Add $2$ and $4$ .

$\frac{1}{{(\frac{1}{5})}^{6}}$

Step 4

Simplify the denominator.

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Step 4.1

Apply the product rule to $\frac{1}{5}$ .

$\frac{1}{\frac{1^{6}}{5^{6}}}$

Step 4.2

One to any power is one.

$\frac{1}{\frac{1}{5^{6}}}$

Step 4.3

Raise $5$ to the power of $6$ .

$\frac{1}{\frac{1}{15625}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$1 \cdot 15625$

Step 6

Multiply $15625$ by $1$ .

$15625$