Basic Math Examples

$\frac{2^{\frac{5}{2}}}{8^{\frac{1}{3}}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $8$ as $2^{3}$ .

$\frac{2^{\frac{5}{2}}}{{(2^{3})}^{\frac{1}{3}}}$

Step 1.2

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

$\frac{2^{\frac{5}{2}}}{2^{3 (\frac{1}{3})}}$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Cancel the common factor.

$\frac{2^{\frac{5}{2}}}{2^{3 (\frac{1}{3})}}$

Step 1.3.2

Rewrite the expression.

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

Step 1.4

Evaluate the exponent.

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3.3

Combine $- 1$ and $\frac{2}{2}$ .

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 1$ by $2$ .

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

Step 3.5.2

Subtract $2$ from $5$ .

$2^{\frac{3}{2}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2^{\frac{3}{2}}$

Decimal Form:

$2.82842712 \dots$