Simplify (5^( square root of 3+2))/(5^( square root of 3-2))

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

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

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

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

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

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

Simplify each term.

Apply the distributive property.

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

Multiply $- 1$ by $- 2$ .

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

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

$5^{0 + 2 + 2}$

Add $0$ and $2$ .

$5^{2 + 2}$

Add $2$ and $2$ .

$5^{4}$

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

$625$