Algebra Examples

$x + 5 = 4^{\frac{3}{2}}$

Step 1

Simplify $4^{\frac{3}{2}}$ .

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Step 1.1

Rewrite.

$x + 5 = 0 + 0 + 4^{\frac{3}{2}}$

Step 1.2

Simplify the expression.

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Step 1.2.1

Rewrite $4$ as $2^{2}$ .

$x + 5 = {(2^{2})}^{\frac{3}{2}}$

Step 1.2.2

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

$x + 5 = 2^{2 (\frac{3}{2})}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Cancel the common factor.

$x + 5 = 2^{2 (\frac{3}{2})}$

Step 1.3.2

Rewrite the expression.

$x + 5 = 2^{3}$

Step 1.4

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

$x + 5 = 8$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Subtract $5$ from both sides of the equation.

$x = 8 - 5$

Step 2.2

Subtract $5$ from $8$ .

$x = 3$