Algebra Examples

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

Step 1

Multiply $5 (- \frac{1}{2})$ .

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Step 1.1

Multiply $- 1$ by $5$ .

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

Step 1.2

Combine $- 5$ and $\frac{1}{2}$ .

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

Step 2

Move the negative in front of the fraction.

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

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 4

Apply the product rule to $\frac{5}{6}$ .

$\frac{5^{\frac{5}{2}}}{6^{\frac{5}{2}}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5^{\frac{5}{2}}}{6^{\frac{5}{2}}}$

Decimal Form:

$0.63393814 \dots$