Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 1.2.2

Factor $2$ out of $- 6$ .

$5^{2 (- 3) \frac{- 1}{2}}$

Step 1.2.3

Cancel the common factor.

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

Step 1.2.4

Rewrite the expression.

$5^{- 3 \cdot - 1}$

Step 1.3

Multiply $- 3$ by $- 1$ .

$5^{3}$

Step 2

Raise $5$ to the power of $3$ .

$125$