Evaluate (16^(5/4)*16^(1/4))/((16^(1/2))^2)

$\frac{16^{\frac{5}{4}} \cdot 16^{\frac{1}{4}}}{{(16^{\frac{1}{2}})}^{2}}$

Step 1

Multiply $16^{\frac{5}{4}}$ by $16^{\frac{1}{4}}$ by adding the exponents.

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

$\frac{16^{\frac{5}{4} + \frac{1}{4}}}{{(16^{\frac{1}{2}})}^{2}}$

Combine the numerators over the common denominator.

$\frac{16^{\frac{5 + 1}{4}}}{{(16^{\frac{1}{2}})}^{2}}$

Add $5$ and $1$ .

$\frac{16^{\frac{6}{4}}}{{(16^{\frac{1}{2}})}^{2}}$

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Simplify the numerator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Raise $4$ to the power of $3$ .

$\frac{64}{{(16^{\frac{1}{2}})}^{2}}$

Step 3

Simplify the denominator.

Multiply the exponents in ${(16^{\frac{1}{2}})}^{2}$ .

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

$\frac{64}{16^{\frac{1}{2} \cdot 2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{64}{16^{\frac{1}{2} \cdot 2}}$

Rewrite the expression.

$\frac{64}{16^{1}}$

Evaluate the exponent.

$\frac{64}{16}$

Step 4

Divide $64$ by $16$ .

$4$

Evaluate (16^(5/4)*16^(1/4))/((16^(1/2))^2)

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