Simplify (3x^-6y^-3)/(15x^2y^10)

$\frac{3 x^{- 6} y^{- 3}}{15 x^{2} y^{10}}$

Step 1

Move $x^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3 y^{- 3}}{15 x^{2} y^{10} x^{6}}$

Step 2

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

$\frac{3}{15 x^{2} y^{10} x^{6} y^{3}}$

Step 3

Simplify the denominator.

Multiply $x^{2}$ by $x^{6}$ by adding the exponents.

Move $x^{6}$ .

$\frac{3}{15 (x^{6} x^{2}) y^{10} y^{3}}$

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

$\frac{3}{15 x^{6 + 2} y^{10} y^{3}}$

Add $6$ and $2$ .

$\frac{3}{15 x^{8} y^{10} y^{3}}$

Multiply $y^{10}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$\frac{3}{15 x^{8} (y^{3} y^{10})}$

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

$\frac{3}{15 x^{8} y^{3 + 10}}$

Add $3$ and $10$ .

$\frac{3}{15 x^{8} y^{13}}$

Step 4

Cancel the common factor of $3$ and $15$ .

Factor $3$ out of $3$ .

$\frac{3 (1)}{15 x^{8} y^{13}}$

Cancel the common factors.

Factor $3$ out of $15 x^{8} y^{13}$ .

$\frac{3 (1)}{3 (5 x^{8} y^{13})}$

Cancel the common factor.

$\frac{3 \cdot 1}{3 (5 x^{8} y^{13})}$

Rewrite the expression.

$\frac{1}{5 x^{8} y^{13}}$