Simplify -3(2x^4)(4x^5y)^2

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

Step 1

Multiply $2$ by $- 3$ .

$- 6 x^{4} {(4 x^{5} y)}^{2}$

Step 2

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

Apply the product rule to $4 x^{5} y$ .

$- 6 x^{4} ({(4 x^{5})}^{2} y^{2})$

Apply the product rule to $4 x^{5}$ .

$- 6 x^{4} (4^{2} {(x^{5})}^{2} y^{2})$

Step 3

Raise $4$ to the power of $2$ .

$- 6 x^{4} (16 {(x^{5})}^{2} y^{2})$

Step 4

Multiply the exponents in ${(x^{5})}^{2}$ .

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

$- 6 x^{4} (16 x^{5 \cdot 2} y^{2})$

Multiply $5$ by $2$ .

$- 6 x^{4} (16 x^{10} y^{2})$

Step 5

Multiply $x^{4}$ by $x^{10}$ by adding the exponents.

Move $x^{10}$ .

$- 6 (x^{10} x^{4}) (16 y^{2})$

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

$- 6 x^{10 + 4} (16 y^{2})$

Add $10$ and $4$ .

$- 6 x^{14} (16 y^{2})$

Step 6

Rewrite using the commutative property of multiplication.

$- 6 \cdot 16 x^{14} y^{2}$

Step 7

Multiply $- 6$ by $16$ .

$- 96 x^{14} y^{2}$