Solve for n (n+3)^(5/4)-32=0

${(n + 3)}^{\frac{5}{4}} - 32 = 0$

Step 1

Add $32$ to both sides of the equation.

${(n + 3)}^{\frac{5}{4}} = 32$

Step 2

Raise each side of the equation to the power of $\frac{4}{5}$ to eliminate the fractional exponent on the left side.

${({(n + 3)}^{\frac{5}{4}})}^{\frac{4}{5}} = 32^{\frac{4}{5}}$

Step 3

Simplify the exponent.

Simplify the left side.

Simplify ${({(n + 3)}^{\frac{5}{4}})}^{\frac{4}{5}}$ .

Multiply the exponents in ${({(n + 3)}^{\frac{5}{4}})}^{\frac{4}{5}}$ .

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

${(n + 3)}^{\frac{5}{4} \cdot \frac{4}{5}} = 32^{\frac{4}{5}}$

Cancel the common factor of $5$ .

Cancel the common factor.

${(n + 3)}^{\frac{5}{4} \cdot \frac{4}{5}} = 32^{\frac{4}{5}}$

Rewrite the expression.

${(n + 3)}^{\frac{1}{4} \cdot 4} = 32^{\frac{4}{5}}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(n + 3)}^{\frac{1}{4} \cdot 4} = 32^{\frac{4}{5}}$

Rewrite the expression.

${(n + 3)}^{1} = 32^{\frac{4}{5}}$

Simplify.

$n + 3 = 32^{\frac{4}{5}}$

Simplify the right side.

Simplify $32^{\frac{4}{5}}$ .

Simplify the expression.

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

$n + 3 = {(2^{5})}^{\frac{4}{5}}$

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

$n + 3 = 2^{5 (\frac{4}{5})}$

Cancel the common factor of $5$ .

Cancel the common factor.

$n + 3 = 2^{5 (\frac{4}{5})}$

Rewrite the expression.

$n + 3 = 2^{4}$

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

$n + 3 = 16$

Step 4

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

Subtract $3$ from both sides of the equation.

$n = 16 - 3$

Subtract $3$ from $16$ .

$n = 13$

Solve for n (n+3)^(5/4)-32=0

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