Precalculus Examples

${(u - 6)}^{\frac{3}{2}} = 2$

Step 1

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

${({(u - 6)}^{\frac{3}{2}})}^{\frac{2}{3}} = 2^{\frac{2}{3}}$

Step 2

Simplify the left side.

Tap for more steps...

Step 2.1

Simplify ${({(u - 6)}^{\frac{3}{2}})}^{\frac{2}{3}}$ .

Tap for more steps...

Step 2.1.1

Multiply the exponents in ${({(u - 6)}^{\frac{3}{2}})}^{\frac{2}{3}}$ .

Tap for more steps...

Step 2.1.1.1

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

${(u - 6)}^{\frac{3}{2} \cdot \frac{2}{3}} = 2^{\frac{2}{3}}$

Step 2.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.1.1.2.1

Cancel the common factor.

${(u - 6)}^{\frac{3}{2} \cdot \frac{2}{3}} = 2^{\frac{2}{3}}$

Step 2.1.1.2.2

Rewrite the expression.

${(u - 6)}^{\frac{1}{2} \cdot 2} = 2^{\frac{2}{3}}$

Step 2.1.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1.3.1

Cancel the common factor.

${(u - 6)}^{\frac{1}{2} \cdot 2} = 2^{\frac{2}{3}}$

Step 2.1.1.3.2

Rewrite the expression.

${(u - 6)}^{1} = 2^{\frac{2}{3}}$

Step 2.1.2

Simplify.

$u - 6 = 2^{\frac{2}{3}}$

Step 3

Add $6$ to both sides of the equation.

$u = 2^{\frac{2}{3}} + 6$

Step 4

The result can be shown in multiple forms.

Exact Form:

$u = 2^{\frac{2}{3}} + 6$

Decimal Form:

$u = 7.58740105 \dots$