Evaluate (5^2y^-10)/(5^-1z^0x^-5)

$\frac{5^{2} y^{- 10}}{5^{- 1} z^{0} x^{- 5}}$

Step 1

Move $y^{- 10}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{5^{2}}{5^{- 1} z^{0} x^{- 5} y^{10}}$

Step 2

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

$\frac{5^{2} \cdot 5}{x^{- 5} y^{10}}$

Step 3

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

$\frac{5^{2} \cdot 5 x^{5}}{y^{10}}$

Step 4

Multiply $5^{2}$ by $5$ by adding the exponents.

Multiply $5^{2}$ by $5$ .

Raise $5$ to the power of $1$ .

$\frac{5^{2} \cdot 5^{1} x^{5}}{y^{10}}$

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

$\frac{5^{2 + 1} x^{5}}{y^{10}}$

Add $2$ and $1$ .

$\frac{5^{3} x^{5}}{y^{10}}$

Step 5

Raise $5$ to the power of $3$ .

$\frac{125 x^{5}}{y^{10}}$