Algebra Examples

${(16^{- \frac{1}{6}} \cdot 9^{\frac{1}{6}})}^{2}$

Step 1

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

${(\frac{1}{16^{\frac{1}{6}}} \cdot 9^{\frac{1}{6}})}^{2}$

Step 2

Combine $\frac{1}{16^{\frac{1}{6}}}$ and $9^{\frac{1}{6}}$ .

${(\frac{9^{\frac{1}{6}}}{16^{\frac{1}{6}}})}^{2}$

Step 3

Apply basic rules of exponents.

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Step 3.1

Apply the product rule to $\frac{9^{\frac{1}{6}}}{16^{\frac{1}{6}}}$ .

$\frac{{(9^{\frac{1}{6}})}^{2}}{{(16^{\frac{1}{6}})}^{2}}$

Step 3.2

Multiply the exponents in ${(9^{\frac{1}{6}})}^{2}$ .

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Step 3.2.1

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

$\frac{9^{\frac{1}{6} \cdot 2}}{{(16^{\frac{1}{6}})}^{2}}$

Step 3.2.2

Cancel the common factor of $2$ .

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Step 3.2.2.1

Factor $2$ out of $6$ .

$\frac{9^{\frac{1}{2 (3)} \cdot 2}}{{(16^{\frac{1}{6}})}^{2}}$

Step 3.2.2.2

Cancel the common factor.

$\frac{9^{\frac{1}{2 \cdot 3} \cdot 2}}{{(16^{\frac{1}{6}})}^{2}}$

Step 3.2.2.3

Rewrite the expression.

$\frac{9^{\frac{1}{3}}}{{(16^{\frac{1}{6}})}^{2}}$

Step 3.3

Multiply the exponents in ${(16^{\frac{1}{6}})}^{2}$ .

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Step 3.3.1

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

$\frac{9^{\frac{1}{3}}}{16^{\frac{1}{6} \cdot 2}}$

Step 3.3.2

Cancel the common factor of $2$ .

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Step 3.3.2.1

Factor $2$ out of $6$ .

$\frac{9^{\frac{1}{3}}}{16^{\frac{1}{2 (3)} \cdot 2}}$

Step 3.3.2.2

Cancel the common factor.

$\frac{9^{\frac{1}{3}}}{16^{\frac{1}{2 \cdot 3} \cdot 2}}$

Step 3.3.2.3

Rewrite the expression.

$\frac{9^{\frac{1}{3}}}{16^{\frac{1}{3}}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{9^{\frac{1}{3}}}{16^{\frac{1}{3}}}$

Decimal Form:

$0.82548181 \dots$