Simplify 1.5m^7(-4m^5)^2

$1.5 m^{7} {(- 4 m^{5})}^{2}$

Step 1

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

$1.5 m^{7} ({(- 4)}^{2} {(m^{5})}^{2})$

Step 2

Rewrite using the commutative property of multiplication.

$1.5 \cdot {(- 4)}^{2} m^{7} {(m^{5})}^{2}$

Step 3

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

$1.5 \cdot 16 m^{7} {(m^{5})}^{2}$

Step 4

Multiply $1.5$ by $16$ .

$24 m^{7} {(m^{5})}^{2}$

Step 5

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

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

$24 m^{7} m^{5 \cdot 2}$

Multiply $5$ by $2$ .

$24 m^{7} m^{10}$

Step 6

Multiply $m^{7}$ by $m^{10}$ by adding the exponents.

Move $m^{10}$ .

$24 (m^{10} m^{7})$

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

$24 m^{10 + 7}$

Add $10$ and $7$ .

$24 m^{17}$