Evaluate 2(48/3)^(-1/4)

$2 {(\frac{48}{3})}^{- \frac{1}{4}}$

Step 1

Divide $48$ by $3$ .

$2 \cdot 16^{- \frac{1}{4}}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$2 \cdot \frac{1}{16^{\frac{1}{4}}}$

Step 3

Simplify the denominator.

Rewrite $16$ as $2^{4}$ .

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$2 \cdot \frac{1}{2^{1}}$

Evaluate the exponent.

$2 \cdot \frac{1}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \cdot \frac{1}{2}$

Rewrite the expression.

$1$