Algebra Examples

$4 x^{\frac{3}{2}} = 32$

Step 1

Divide each term in $4 x^{\frac{3}{2}} = 32$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 x^{\frac{3}{2}} = 32$ by $4$ .

$\frac{4 x^{\frac{3}{2}}}{4} = \frac{32}{4}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor.

$\frac{4 x^{\frac{3}{2}}}{4} = \frac{32}{4}$

Step 1.2.2

Divide $x^{\frac{3}{2}}$ by $1$ .

$x^{\frac{3}{2}} = \frac{32}{4}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $32$ by $4$ .

$x^{\frac{3}{2}} = 8$

Step 2

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

${(x^{\frac{3}{2}})}^{\frac{2}{3}} = 8^{\frac{2}{3}}$

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 ${(x^{\frac{3}{2}})}^{\frac{2}{3}}$ .

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Step 3.1.1.1

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

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Step 3.1.1.1.1

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

$x^{\frac{3}{2} \cdot \frac{2}{3}} = 8^{\frac{2}{3}}$

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.

$x^{\frac{3}{2} \cdot \frac{2}{3}} = 8^{\frac{2}{3}}$

Step 3.1.1.1.2.2

Rewrite the expression.

$x^{\frac{1}{2} \cdot 2} = 8^{\frac{2}{3}}$

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.

$x^{\frac{1}{2} \cdot 2} = 8^{\frac{2}{3}}$

Step 3.1.1.1.3.2

Rewrite the expression.

$x^{1} = 8^{\frac{2}{3}}$

Step 3.1.1.2

Simplify.

$x = 8^{\frac{2}{3}}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $8^{\frac{2}{3}}$ .

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Step 3.2.1.1

Simplify the expression.

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Step 3.2.1.1.1

Rewrite $8$ as $2^{3}$ .

$x = {(2^{3})}^{\frac{2}{3}}$

Step 3.2.1.1.2

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

$x = 2^{3 (\frac{2}{3})}$

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.

$x = 2^{3 (\frac{2}{3})}$

Step 3.2.1.2.2

Rewrite the expression.

$x = 2^{2}$

Step 3.2.1.3

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

$x = 4$