Solve for c (c+1)^(3/2)=64

${(c + 1)}^{\frac{3}{2}} = 64$

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

${({(c + 1)}^{\frac{3}{2}})}^{\frac{2}{3}} = {(64)}^{\frac{2}{3}}$

Solve the equation for $c$ .

Tap for more steps…

Simplify ${(64)}^{\frac{2}{3}}$ .

Tap for more steps…

Simplify the expression.

Tap for more steps…

Rewrite $64$ as $4^{3}$ .

$c + 1 = {(4^{3})}^{\frac{2}{3}}$

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

$c + 1 = 4^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Tap for more steps…

Cancel the common factor.

$c + 1 = 4^{3 (\frac{2}{3})}$

Rewrite the expression.

$c + 1 = 4^{2}$

Raise $4$ to the power of $2$ .

$c + 1 = 16$

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

Tap for more steps…

Subtract $1$ from both sides of the equation.

$c = 16 - 1$

Subtract $1$ from $16$ .

$c = 15$

Solve for c (c+1)^(3/2)=64

Our Professionals