Simplify (2/3x^5y^-5)*(1/3x^2y^2)

$(\frac{2}{3} x^{5} y^{- 5}) \cdot (\frac{1}{3} x^{2} y^{2})$

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

Move $x^{2}$ .

$\frac{2}{3} \cdot (x^{2} x^{5} y^{- 5}) \cdot (\frac{1}{3} \cdot (y^{2}))$

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

$\frac{2}{3} \cdot (x^{2 + 5} y^{- 5}) \cdot (\frac{1}{3} \cdot (y^{2}))$

Add $2$ and $5$ .

$\frac{2}{3} \cdot (x^{7} y^{- 5}) \cdot (\frac{1}{3} \cdot (y^{2}))$

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

Move $y^{2}$ .

$\frac{2}{3} \cdot (x^{7} (y^{2} y^{- 5})) \cdot \frac{1}{3}$

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

$\frac{2}{3} \cdot (x^{7} y^{2 - 5}) \cdot \frac{1}{3}$

Subtract $5$ from $2$ .

$\frac{2}{3} \cdot (x^{7} y^{- 3}) \cdot \frac{1}{3}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2}{3} \cdot (x^{7} \frac{1}{y^{3}}) \cdot \frac{1}{3}$

Combine $x^{7}$ and $\frac{1}{y^{3}}$ .

$\frac{2}{3} \cdot \frac{x^{7}}{y^{3}} \cdot \frac{1}{3}$

Combine.

$\frac{2 x^{7}}{3 y^{3}} \cdot \frac{1}{3}$

Combine.

$\frac{2 x^{7} \cdot 1}{3 y^{3} \cdot 3}$

Multiply.

Multiply $2$ by $1$ .

$\frac{2 x^{7}}{3 y^{3} \cdot 3}$

Multiply $3$ by $3$ .

$\frac{2 x^{7}}{9 y^{3}}$