Basic Math Examples

$64 = y^{\frac{3}{2}}$

Step 1

Rewrite the equation as $y^{\frac{3}{2}} = 64$ .

$y^{\frac{3}{2}} = 64$

Step 2

Raise each side of the equation to the power of $\frac{2}{3}$ to eliminate the fractional exponent on the left side.

${(y^{\frac{3}{2}})}^{\frac{2}{3}} = 64^{\frac{2}{3}}$

Step 3

Simplify the exponent.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify ${(y^{\frac{3}{2}})}^{\frac{2}{3}}$ .

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Step 3.1.1.1

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

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Step 3.1.1.1.1

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

$y^{\frac{3}{2} \cdot \frac{2}{3}} = 64^{\frac{2}{3}}$

Step 3.1.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.1.2.1

Cancel the common factor.

$y^{\frac{3}{2} \cdot \frac{2}{3}} = 64^{\frac{2}{3}}$

Step 3.1.1.1.2.2

Rewrite the expression.

$y^{\frac{1}{2} \cdot 2} = 64^{\frac{2}{3}}$

Step 3.1.1.1.3

Cancel the common factor of $2$ .

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Step 3.1.1.1.3.1

Cancel the common factor.

$y^{\frac{1}{2} \cdot 2} = 64^{\frac{2}{3}}$

Step 3.1.1.1.3.2

Rewrite the expression.

$y^{1} = 64^{\frac{2}{3}}$

Step 3.1.1.2

Simplify.

$y = 64^{\frac{2}{3}}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $64^{\frac{2}{3}}$ .

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Step 3.2.1.1

Simplify the expression.

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Step 3.2.1.1.1

Rewrite $64$ as $4^{3}$ .

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

Step 3.2.1.1.2

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

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

Step 3.2.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.2.1

Cancel the common factor.

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

Step 3.2.1.2.2

Rewrite the expression.

$y = 4^{2}$

Step 3.2.1.3

Raise $4$ to the power of $2$ .

$y = 16$