Algebra Examples

${(7^{\frac{3}{4}})}^{- \frac{2}{9}}$

Step 1

Multiply the exponents in ${(7^{\frac{3}{4}})}^{- \frac{2}{9}}$ .

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Step 1.1

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

$7^{\frac{3}{4} (- \frac{2}{9})}$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Move the leading negative in $- \frac{2}{9}$ into the numerator.

$7^{\frac{3}{4} \cdot \frac{- 2}{9}}$

Step 1.2.2

Factor $3$ out of $9$ .

$7^{\frac{3}{4} \cdot \frac{- 2}{3 (3)}}$

Step 1.2.3

Cancel the common factor.

$7^{\frac{3}{4} \cdot \frac{- 2}{3 \cdot 3}}$

Step 1.2.4

Rewrite the expression.

$7^{\frac{1}{4} \cdot \frac{- 2}{3}}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $4$ .

$7^{\frac{1}{2 (2)} \cdot \frac{- 2}{3}}$

Step 1.3.2

Factor $2$ out of $- 2$ .

$7^{\frac{1}{2 \cdot 2} \cdot \frac{2 \cdot - 1}{3}}$

Step 1.3.3

Cancel the common factor.

$7^{\frac{1}{2 \cdot 2} \cdot \frac{2 \cdot - 1}{3}}$

Step 1.3.4

Rewrite the expression.

$7^{\frac{1}{2} \cdot \frac{- 1}{3}}$

Step 1.4

Multiply $\frac{1}{2}$ by $\frac{- 1}{3}$ .

$7^{\frac{- 1}{2 \cdot 3}}$

Step 1.5

Multiply $2$ by $3$ .

$7^{\frac{- 1}{6}}$

Step 1.6

Move the negative in front of the fraction.

$7^{- \frac{1}{6}}$

Step 2

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

$\frac{1}{7^{\frac{1}{6}}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{7^{\frac{1}{6}}}$

Decimal Form:

$0.72302002 \dots$