Simplify 1.5m^6(-2m^2)^4

$1.5 m^{6} {(- 2 m^{2})}^{4}$

Step 1

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

$1.5 m^{6} ({(- 2)}^{4} {(m^{2})}^{4})$

Step 2

Rewrite using the commutative property of multiplication.

$1.5 \cdot {(- 2)}^{4} m^{6} {(m^{2})}^{4}$

Step 3

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

$1.5 \cdot 16 m^{6} {(m^{2})}^{4}$

Step 4

Multiply $1.5$ by $16$ .

$24 m^{6} {(m^{2})}^{4}$

Step 5

Multiply the exponents in ${(m^{2})}^{4}$ .

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

$24 m^{6} m^{2 \cdot 4}$

Multiply $2$ by $4$ .

$24 m^{6} m^{8}$

Step 6

Multiply $m^{6}$ by $m^{8}$ by adding the exponents.

Move $m^{8}$ .

$24 (m^{8} m^{6})$

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

$24 m^{8 + 6}$

Add $8$ and $6$ .

$24 m^{14}$