Precalculus Examples

$27 = x^{\frac{3}{2}}$

Step 1

Rewrite the equation as $x^{\frac{3}{2}} = 27$ .

$x^{\frac{3}{2}} = 27$

Step 2

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

${(x^{\frac{3}{2}})}^{\frac{2}{3}} = 27^{\frac{2}{3}}$

Step 3

Simplify the exponent.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

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

Tap for more steps...

Step 3.1.1.1

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

Tap for more steps...

Step 3.1.1.1.1

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

$x^{\frac{3}{2} \cdot \frac{2}{3}} = 27^{\frac{2}{3}}$

Step 3.1.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1.1.1.2.1

Cancel the common factor.

$x^{\frac{3}{2} \cdot \frac{2}{3}} = 27^{\frac{2}{3}}$

Step 3.1.1.1.2.2

Rewrite the expression.

$x^{\frac{1}{2} \cdot 2} = 27^{\frac{2}{3}}$

Step 3.1.1.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.1.1.3.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 27^{\frac{2}{3}}$

Step 3.1.1.1.3.2

Rewrite the expression.

$x^{1} = 27^{\frac{2}{3}}$

Step 3.1.1.2

Simplify.

$x = 27^{\frac{2}{3}}$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify $27^{\frac{2}{3}}$ .

Tap for more steps...

Step 3.2.1.1

Simplify the expression.

Tap for more steps...

Step 3.2.1.1.1

Rewrite $27$ as $3^{3}$ .

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

Step 3.2.1.1.2

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

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

Step 3.2.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1.2.1

Cancel the common factor.

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

Step 3.2.1.2.2

Rewrite the expression.

$x = 3^{2}$

Step 3.2.1.3

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

$x = 9$