Simplify ((16x^2)^(1/4))/((16x^2)^(3/4))

$\frac{{(16 x^{2})}^{\frac{1}{4}}}{{(16 x^{2})}^{\frac{3}{4}}}$

Step 1

Move ${(16 x^{2})}^{\frac{1}{4}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{1}{{(16 x^{2})}^{\frac{3}{4}} {(16 x^{2})}^{- \frac{1}{4}}}$

Step 2

Multiply ${(16 x^{2})}^{\frac{3}{4}}$ by ${(16 x^{2})}^{- \frac{1}{4}}$ by adding the exponents.

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

$\frac{1}{{(16 x^{2})}^{\frac{3}{4} - \frac{1}{4}}}$

Combine the numerators over the common denominator.

$\frac{1}{{(16 x^{2})}^{\frac{3 - 1}{4}}}$

Subtract $1$ from $3$ .

$\frac{1}{{(16 x^{2})}^{\frac{2}{4}}}$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$\frac{1}{{(16 x^{2})}^{\frac{2 (1)}{4}}}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{1}{{(16 x^{2})}^{\frac{2 \cdot 1}{2 \cdot 2}}}$

Cancel the common factor.

$\frac{1}{{(16 x^{2})}^{\frac{2 \cdot 1}{2 \cdot 2}}}$

Rewrite the expression.

$\frac{1}{{(16 x^{2})}^{\frac{1}{2}}}$

Step 3

Simplify the denominator.

Apply the product rule to $16 x^{2}$ .

$\frac{1}{16^{\frac{1}{2}} {(x^{2})}^{\frac{1}{2}}}$

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Multiply the exponents in ${(x^{2})}^{\frac{1}{2}}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$\frac{1}{4 x}$

Simplify ((16x^2)^(1/4))/((16x^2)^(3/4))

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