Simplify (8^-2x^-3y^11)/(x^2y^-5)

$\frac{8^{- 2} x^{- 3} y^{11}}{x^{2} y^{- 5}}$

Step 1

Move $8^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{- 3} y^{11}}{x^{2} y^{- 5} \cdot 8^{2}}$

Step 2

Move $x^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{y^{11}}{x^{2} y^{- 5} \cdot 8^{2} x^{3}}$

Step 3

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\frac{y^{11}}{x^{3} x^{2} y^{- 5} \cdot 8^{2}}$

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

$\frac{y^{11}}{x^{3 + 2} y^{- 5} \cdot 8^{2}}$

Add $3$ and $2$ .

$\frac{y^{11}}{x^{5} y^{- 5} \cdot 8^{2}}$

Step 4

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

$\frac{y^{11} y^{5}}{x^{5} \cdot 8^{2}}$

Step 5

Multiply $y^{11}$ by $y^{5}$ by adding the exponents.

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

$\frac{y^{11 + 5}}{x^{5} \cdot 8^{2}}$

Add $11$ and $5$ .

$\frac{y^{16}}{x^{5} \cdot 8^{2}}$

Step 6

Raise $8$ to the power of $2$ .

$\frac{y^{16}}{x^{5} \cdot 64}$

Step 7

Move $64$ to the left of $x^{5}$ .

$\frac{y^{16}}{64 x^{5}}$