Algebra Examples

$- {(2 p^{4})}^{3} (- 1.5 p^{7})$

Step 1

Rewrite using the commutative property of multiplication.

$- 1 \cdot - 1.5 {(2 p^{4})}^{3} p^{7}$

Step 2

Multiply $- 1$ by $- 1.5$ .

$1.5 {(2 p^{4})}^{3} p^{7}$

Step 3

Apply the product rule to $2 p^{4}$ .

$1.5 (2^{3} {(p^{4})}^{3}) p^{7}$

Step 4

Raise $2$ to the power of $3$ .

$1.5 (8 {(p^{4})}^{3}) p^{7}$

Step 5

Multiply the exponents in ${(p^{4})}^{3}$ .

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Step 5.1

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

$1.5 (8 p^{4 \cdot 3}) p^{7}$

Step 5.2

Multiply $4$ by $3$ .

$1.5 (8 p^{12}) p^{7}$

Step 6

Multiply $p^{12}$ by $p^{7}$ by adding the exponents.

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Step 6.1

Move $p^{7}$ .

$1.5 (8 (p^{7} p^{12}))$

Step 6.2

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

$1.5 (8 p^{7 + 12})$

Step 6.3

Add $7$ and $12$ .

$1.5 (8 p^{19})$

Step 7

Multiply $8$ by $1.5$ .

$12 p^{19}$