Algebra Examples

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

Step 1

Subtract $16$ from both sides of the equation.

$\frac{1}{2} x^{\frac{5}{2}} - 16 = 0$

Step 2

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

$\frac{x^{\frac{5}{2}}}{2} - 16 = 0$

Step 3

To write $- 16$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x^{\frac{5}{2}}}{2} - 16 \cdot \frac{2}{2} = 0$

Step 4

Combine $- 16$ and $\frac{2}{2}$ .

$\frac{x^{\frac{5}{2}}}{2} + \frac{- 16 \cdot 2}{2} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{x^{\frac{5}{2}} - 16 \cdot 2}{2} = 0$

Step 6

Multiply $- 16$ by $2$ .

$\frac{x^{\frac{5}{2}} - 32}{2} = 0$

Step 7

Set the numerator equal to zero.

$x^{\frac{5}{2}} - 32 = 0$

Step 8

Solve the equation for $x$ .

Tap for more steps...

Step 8.1

Add $32$ to both sides of the equation.

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

Step 8.2

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 8.3

Simplify the exponent.

Tap for more steps...

Step 8.3.1

Simplify the left side.

Tap for more steps...

Step 8.3.1.1

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

Tap for more steps...

Step 8.3.1.1.1

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

Tap for more steps...

Step 8.3.1.1.1.1

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 8.3.1.1.1.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 8.3.1.1.1.2.1

Cancel the common factor.

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

Step 8.3.1.1.1.2.2

Rewrite the expression.

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

Step 8.3.1.1.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 8.3.1.1.1.3.1

Cancel the common factor.

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

Step 8.3.1.1.1.3.2

Rewrite the expression.

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

Step 8.3.1.1.2

Simplify.

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

Step 8.3.2

Simplify the right side.

Tap for more steps...

Step 8.3.2.1

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

Tap for more steps...

Step 8.3.2.1.1

Simplify the expression.

Tap for more steps...

Step 8.3.2.1.1.1

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

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

Step 8.3.2.1.1.2

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

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

Step 8.3.2.1.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 8.3.2.1.2.1

Cancel the common factor.

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

Step 8.3.2.1.2.2

Rewrite the expression.

$x = 2^{2}$

Step 8.3.2.1.3

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

$x = 4$