Simplify -(7x^3y)^2

$- {(7 x^{3} y)}^{2}$

Step 1

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

Apply the product rule to $7 x^{3} y$ .

$- ({(7 x^{3})}^{2} y^{2})$

Apply the product rule to $7 x^{3}$ .

$- (7^{2} {(x^{3})}^{2} y^{2})$

Step 2

Raise $7$ to the power of $2$ .

$- (49 {(x^{3})}^{2} y^{2})$

Step 3

Multiply the exponents in ${(x^{3})}^{2}$ .

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

$- (49 x^{3 \cdot 2} y^{2})$

Multiply $3$ by $2$ .

$- (49 x^{6} y^{2})$

Step 4

Multiply $49$ by $- 1$ .

$- 49 x^{6} y^{2}$