Algebra Examples

$\frac{1}{2} x^{\frac{5}{2}} = 16$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} x^{\frac{5}{2}}) = 2 \cdot 16$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $2 (\frac{1}{2} x^{\frac{5}{2}})$ .

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Step 2.1.1.1

Combine $\frac{1}{2}$ and $x^{\frac{5}{2}}$ .

$2 \frac{x^{\frac{5}{2}}}{2} = 2 \cdot 16$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Cancel the common factor.

$2 \frac{x^{\frac{5}{2}}}{2} = 2 \cdot 16$

Step 2.1.1.2.2

Rewrite the expression.

$x^{\frac{5}{2}} = 2 \cdot 16$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $16$ .

$x^{\frac{5}{2}} = 32$

Step 3

Raise each side of the equation to the power of $\frac{2}{5}$ to eliminate the fractional exponent on the left side.

${(x^{\frac{5}{2}})}^{\frac{2}{5}} = 32^{\frac{2}{5}}$

Step 4

Simplify the exponent.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify ${(x^{\frac{5}{2}})}^{\frac{2}{5}}$ .

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Step 4.1.1.1

Multiply the exponents in ${(x^{\frac{5}{2}})}^{\frac{2}{5}}$ .

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Step 4.1.1.1.1

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

$x^{\frac{5}{2} \cdot \frac{2}{5}} = 32^{\frac{2}{5}}$

Step 4.1.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.1.2.1

Cancel the common factor.

$x^{\frac{5}{2} \cdot \frac{2}{5}} = 32^{\frac{2}{5}}$

Step 4.1.1.1.2.2

Rewrite the expression.

$x^{\frac{1}{2} \cdot 2} = 32^{\frac{2}{5}}$

Step 4.1.1.1.3

Cancel the common factor of $2$ .

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Step 4.1.1.1.3.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 32^{\frac{2}{5}}$

Step 4.1.1.1.3.2

Rewrite the expression.

$x^{1} = 32^{\frac{2}{5}}$

Step 4.1.1.2

Simplify.

$x = 32^{\frac{2}{5}}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $32^{\frac{2}{5}}$ .

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Step 4.2.1.1

Simplify the expression.

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Step 4.2.1.1.1

Rewrite $32$ as $2^{5}$ .

$x = {(2^{5})}^{\frac{2}{5}}$

Step 4.2.1.1.2

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

$x = 2^{5 (\frac{2}{5})}$

Step 4.2.1.2

Cancel the common factor of $5$ .

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Step 4.2.1.2.1

Cancel the common factor.

$x = 2^{5 (\frac{2}{5})}$

Step 4.2.1.2.2

Rewrite the expression.

$x = 2^{2}$

Step 4.2.1.3

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

$x = 4$