Simplify 3x^2(5xy)^2(xy)^-1

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Apply the product rule to $5 x y$ .

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

Apply the product rule to $5 x$ .

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

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

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Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

$3 x^{4} (5^{2} y^{2}) {(x y)}^{- 1}$

Rewrite using the commutative property of multiplication.

$3 \cdot 5^{2} (x^{4} y^{2}) {(x y)}^{- 1}$

Raise $5$ to the power of $2$ .

$3 \cdot 25 (x^{4} y^{2}) {(x y)}^{- 1}$

Multiply $3$ by $25$ .

$75 (x^{4} y^{2}) {(x y)}^{- 1}$

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

$75 x^{4} y^{2} \frac{1}{x y}$

Cancel the common factor of $x y$ .

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Factor $x y$ out of $75 x^{4} y^{2}$ .

$x y (75 x^{3} y) \frac{1}{x y}$

Cancel the common factor.

$x y (75 x^{3} y) \frac{1}{x y}$

Rewrite the expression.

$75 x^{3} y$

Simplify 3x^2(5xy)^2(xy)^-1