Simplify ((x^6y^3)/(x^3y^-3)*(y^-7)/(x^-3))^10

${(\frac{x^{6} y^{3}}{x^{3} y^{- 3}} \cdot \frac{y^{- 7}}{x^{- 3}})}^{10}$

Step 1

Combine.

${(\frac{x^{6} y^{3} y^{- 7}}{x^{3} y^{- 3} x^{- 3}})}^{10}$

Step 2

Multiply $y^{3}$ by $y^{- 7}$ by adding the exponents.

Move $y^{- 7}$ .

${(\frac{x^{6} (y^{- 7} y^{3})}{x^{3} y^{- 3} x^{- 3}})}^{10}$

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

${(\frac{x^{6} y^{- 7 + 3}}{x^{3} y^{- 3} x^{- 3}})}^{10}$

Add $- 7$ and $3$ .

${(\frac{x^{6} y^{- 4}}{x^{3} y^{- 3} x^{- 3}})}^{10}$

Step 3

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

Move $x^{- 3}$ .

${(\frac{x^{6} y^{- 4}}{x^{- 3} x^{3} y^{- 3}})}^{10}$

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

${(\frac{x^{6} y^{- 4}}{x^{- 3 + 3} y^{- 3}})}^{10}$

Add $- 3$ and $3$ .

${(\frac{x^{6} y^{- 4}}{x^{0} y^{- 3}})}^{10}$

Step 4

Simplify $x^{0} y^{- 3}$ .

${(\frac{x^{6} y^{- 4}}{y^{- 3}})}^{10}$

Step 5

Move $y^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{x^{6}}{y^{- 3} y^{4}})}^{10}$

Step 6

Simplify the denominator.

Multiply $y^{- 3}$ by $y^{4}$ by adding the exponents.

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

${(\frac{x^{6}}{y^{- 3 + 4}})}^{10}$

Add $- 3$ and $4$ .

${(\frac{x^{6}}{y^{1}})}^{10}$

Simplify $y^{1}$ .

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

Step 7

Apply the product rule to $\frac{x^{6}}{y}$ .

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

Step 8

Multiply the exponents in ${(x^{6})}^{10}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{x^{6 \cdot 10}}{y^{10}}$

Multiply $6$ by $10$ .

$\frac{x^{60}}{y^{10}}$