Basic Math Examples

${(2 g^{\frac{4}{3}} y^{\frac{- 2}{3}})}^{3}$

Step 1

Move the negative in front of the fraction.

${(2 g^{\frac{4}{3}} y^{- \frac{2}{3}})}^{3}$

Step 2

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

${(2 g^{\frac{4}{3}} \frac{1}{y^{\frac{2}{3}}})}^{3}$

Step 3

Multiply $2 g^{\frac{4}{3}} \frac{1}{y^{\frac{2}{3}}}$ .

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Step 3.1

Combine $2$ and $\frac{1}{y^{\frac{2}{3}}}$ .

${(g^{\frac{4}{3}} \frac{2}{y^{\frac{2}{3}}})}^{3}$

Step 3.2

Combine $g^{\frac{4}{3}}$ and $\frac{2}{y^{\frac{2}{3}}}$ .

${(\frac{g^{\frac{4}{3}} \cdot 2}{y^{\frac{2}{3}}})}^{3}$

Step 4

Move $2$ to the left of $g^{\frac{4}{3}}$ .

${(\frac{2 \cdot g^{\frac{4}{3}}}{y^{\frac{2}{3}}})}^{3}$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 5.1

Apply the product rule to $\frac{2 g^{\frac{4}{3}}}{y^{\frac{2}{3}}}$ .

$\frac{{(2 g^{\frac{4}{3}})}^{3}}{{(y^{\frac{2}{3}})}^{3}}$

Step 5.2

Apply the product rule to $2 g^{\frac{4}{3}}$ .

$\frac{2^{3} {(g^{\frac{4}{3}})}^{3}}{{(y^{\frac{2}{3}})}^{3}}$

Step 6

Simplify the numerator.

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Step 6.1

Raise $2$ to the power of $3$ .

$\frac{8 {(g^{\frac{4}{3}})}^{3}}{{(y^{\frac{2}{3}})}^{3}}$

Step 6.2

Multiply the exponents in ${(g^{\frac{4}{3}})}^{3}$ .

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Step 6.2.1

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

$\frac{8 g^{\frac{4}{3} \cdot 3}}{{(y^{\frac{2}{3}})}^{3}}$

Step 6.2.2

Cancel the common factor of $3$ .

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Step 6.2.2.1

Cancel the common factor.

$\frac{8 g^{\frac{4}{3} \cdot 3}}{{(y^{\frac{2}{3}})}^{3}}$

Step 6.2.2.2

Rewrite the expression.

$\frac{8 g^{4}}{{(y^{\frac{2}{3}})}^{3}}$

Step 7

Multiply the exponents in ${(y^{\frac{2}{3}})}^{3}$ .

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Step 7.1

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

$\frac{8 g^{4}}{y^{\frac{2}{3} \cdot 3}}$

Step 7.2

Cancel the common factor of $3$ .

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Step 7.2.1

Cancel the common factor.

$\frac{8 g^{4}}{y^{\frac{2}{3} \cdot 3}}$

Step 7.2.2

Rewrite the expression.

$\frac{8 g^{4}}{y^{2}}$