Algebra Examples

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

Step 1

Multiply $16^{5}$ by $16^{\frac{1}{2}}$ by adding the exponents.

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Step 1.1

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

$16^{5 + \frac{1}{2}}$

Step 1.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$16^{5 \cdot \frac{2}{2} + \frac{1}{2}}$

Step 1.3

Combine $5$ and $\frac{2}{2}$ .

$16^{\frac{5 \cdot 2}{2} + \frac{1}{2}}$

Step 1.4

Combine the numerators over the common denominator.

$16^{\frac{5 \cdot 2 + 1}{2}}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $5$ by $2$ .

$16^{\frac{10 + 1}{2}}$

Step 1.5.2

Add $10$ and $1$ .

$16^{\frac{11}{2}}$

Step 2

Simplify the expression.

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Step 2.1

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

${(4^{2})}^{\frac{11}{2}}$

Step 2.2

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

$4^{2 (\frac{11}{2})}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

$4^{2 (\frac{11}{2})}$

Step 3.2

Rewrite the expression.

$4^{11}$

Step 4

Raise $4$ to the power of $11$ .

$4194304$