Algebra Examples

${(5^{\frac{1}{2}} \cdot 5^{- \frac{3}{2}})}^{- \frac{1}{4}}$

Step 1

Multiply $5^{\frac{1}{2}}$ by $5^{- \frac{3}{2}}$ 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.

${(5^{\frac{1}{2} - \frac{3}{2}})}^{- \frac{1}{4}}$

Step 1.2

Combine the numerators over the common denominator.

${(5^{\frac{1 - 3}{2}})}^{- \frac{1}{4}}$

Step 1.3

Subtract $3$ from $1$ .

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

Step 1.4

Divide $- 2$ by $2$ .

${(5^{- 1})}^{- \frac{1}{4}}$

Step 2

Multiply the exponents in ${(5^{- 1})}^{- \frac{1}{4}}$ .

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Step 2.1

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

$5^{- - \frac{1}{4}}$

Step 2.2

Multiply $- - \frac{1}{4}$ .

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Step 2.2.1

Multiply $- 1$ by $- 1$ .

$5^{1 (\frac{1}{4})}$

Step 2.2.2

Multiply $\frac{1}{4}$ by $1$ .

$5^{\frac{1}{4}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5^{\frac{1}{4}}$

Decimal Form:

$1.49534878 \dots$