Algebra Examples

$\frac{8^{\frac{5}{2}}}{8^{\frac{1}{2}}}$

Step 1

Move $8^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$8^{\frac{5}{2}} \cdot 8^{- \frac{1}{2}}$

Step 2

Multiply $8^{\frac{5}{2}}$ by $8^{- \frac{1}{2}}$ by adding the exponents.

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Step 2.1

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

$8^{\frac{5}{2} - \frac{1}{2}}$

Step 2.2

Combine the numerators over the common denominator.

$8^{\frac{5 - 1}{2}}$

Step 2.3

Subtract $1$ from $5$ .

$8^{\frac{4}{2}}$

Step 2.4

Divide $4$ by $2$ .

$8^{2}$

Step 3

Raise $8$ to the power of $2$ .

$64$