Solve for y y=1/4(4)^(3/2)

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

Step 1

Remove parentheses.

$y = \frac{1}{4} \cdot 4^{\frac{3}{2}}$

Step 2

Simplify $\frac{1}{4} \cdot 4^{\frac{3}{2}}$ .

Simplify the expression.

Rewrite $4$ as $2^{2}$ .

$y = \frac{1}{4} \cdot {(2^{2})}^{\frac{3}{2}}$

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

$y = \frac{1}{4} \cdot 2^{2 (\frac{3}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$y = \frac{1}{4} \cdot 2^{2 (\frac{3}{2})}$

Rewrite the expression.

$y = \frac{1}{4} \cdot 2^{3}$

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

$y = \frac{1}{4} \cdot 8$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$y = \frac{1}{4} \cdot (4 (2))$

Cancel the common factor.

$y = \frac{1}{4} \cdot (4 \cdot 2)$

Rewrite the expression.

$y = 2$