Algebra Examples

$\frac{5^{\sqrt{3} + 2}}{5^{\sqrt{3} - 2}}$

Step 1

Move $5^{\sqrt{3} - 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$5^{\sqrt{3} + 2} \cdot 5^{- (\sqrt{3} - 2)}$

Step 2

Multiply $5^{\sqrt{3} + 2}$ by $5^{- (\sqrt{3} - 2)}$ 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.

$5^{\sqrt{3} + 2 - (\sqrt{3} - 2)}$

Step 2.2

Simplify each term.

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Step 2.2.1

Apply the distributive property.

$5^{\sqrt{3} + 2 - \sqrt{3} - - 2}$

Step 2.2.2

Multiply $- 1$ by $- 2$ .

$5^{\sqrt{3} + 2 - \sqrt{3} + 2}$

Step 2.3

Subtract $\sqrt{3}$ from $\sqrt{3}$ .

$5^{0 + 2 + 2}$

Step 2.4

Add $0$ and $2$ .

$5^{2 + 2}$

Step 2.5

Add $2$ and $2$ .

$5^{4}$

Step 3

Raise $5$ to the power of $4$ .

$625$