Simplify (-5x^2y)^2*xy^2-9x^5y^4

${(- 5 x^{2} y)}^{2} \cdot x y^{2} - 9 x^{5} y^{4}$

Step 1

Simplify each term.

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

Apply the product rule to $- 5 x^{2} y$ .

${(- 5 x^{2})}^{2} y^{2} \cdot (x y^{2}) - 9 x^{5} y^{4}$

Apply the product rule to $- 5 x^{2}$ .

${(- 5)}^{2} {(x^{2})}^{2} y^{2} \cdot (x y^{2}) - 9 x^{5} y^{4}$

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

Move $y^{2}$ .

${(- 5)}^{2} {(x^{2})}^{2} (y^{2} y^{2}) \cdot x - 9 x^{5} y^{4}$

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

${(- 5)}^{2} {(x^{2})}^{2} y^{2 + 2} \cdot x - 9 x^{5} y^{4}$

Add $2$ and $2$ .

${(- 5)}^{2} {(x^{2})}^{2} y^{4} \cdot x - 9 x^{5} y^{4}$

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

$25 {(x^{2})}^{2} y^{4} \cdot x - 9 x^{5} y^{4}$

Multiply the exponents in ${(x^{2})}^{2}$ .

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

$25 x^{2 \cdot 2} y^{4} \cdot x - 9 x^{5} y^{4}$

Multiply $2$ by $2$ .

$25 x^{4} y^{4} \cdot x - 9 x^{5} y^{4}$

Multiply $x^{4}$ by $x$ by adding the exponents.

Move $x$ .

$25 (x \cdot x^{4}) y^{4} - 9 x^{5} y^{4}$

Multiply $x$ by $x^{4}$ .

Raise $x$ to the power of $1$ .

$25 (x^{1} x^{4}) y^{4} - 9 x^{5} y^{4}$

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

$25 x^{1 + 4} y^{4} - 9 x^{5} y^{4}$

Add $1$ and $4$ .

$25 x^{5} y^{4} - 9 x^{5} y^{4}$

Step 2

Subtract $9 x^{5} y^{4}$ from $25 x^{5} y^{4}$ .

$16 x^{5} y^{4}$