Evaluate 16/(16^(3/4))

$\frac{16}{16^{\frac{3}{4}}}$

Step 1

Move $16^{\frac{3}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$16 \cdot 16^{- \frac{3}{4}}$

Step 2

Multiply $16$ by $16^{- \frac{3}{4}}$ by adding the exponents.

Multiply $16$ by $16^{- \frac{3}{4}}$ .

Raise $16$ to the power of $1$ .

$16^{1} \cdot 16^{- \frac{3}{4}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$16^{1 - \frac{3}{4}}$

Write $1$ as a fraction with a common denominator.

$16^{\frac{4}{4} - \frac{3}{4}}$

Combine the numerators over the common denominator.

$16^{\frac{4 - 3}{4}}$

Subtract $3$ from $4$ .

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

Step 3

Simplify the expression.

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

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

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

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

Step 4

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$2^{1}$

Step 5

Evaluate the exponent.

$2$