Algebra Examples

${(x^{\frac{5}{6}})}^{- 3}$

Step 1

Multiply the exponents in ${(x^{\frac{5}{6}})}^{- 3}$ .

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Step 1.1

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

$x^{\frac{5}{6} \cdot - 3}$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Factor $3$ out of $6$ .

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

Step 1.2.2

Factor $3$ out of $- 3$ .

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

Step 1.2.3

Cancel the common factor.

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

Step 1.2.4

Rewrite the expression.

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

Step 1.3

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

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

Step 1.4

Multiply $5$ by $- 1$ .

$x^{\frac{- 5}{2}}$

Step 1.5

Move the negative in front of the fraction.

$x^{- \frac{5}{2}}$

Step 2

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

$\frac{1}{x^{\frac{5}{2}}}$