Basic Math Examples

${(8 a)}^{2} {(- a^{3})}^{5}$

Step 1

Apply the product rule to $8 a$ .

$8^{2} a^{2} {(- a^{3})}^{5}$

Step 2

Raise $8$ to the power of $2$ .

$64 a^{2} {(- a^{3})}^{5}$

Step 3

Apply the product rule to $- a^{3}$ .

$64 a^{2} ({(- 1)}^{5} {(a^{3})}^{5})$

Step 4

Rewrite using the commutative property of multiplication.

$64 \cdot {(- 1)}^{5} a^{2} {(a^{3})}^{5}$

Step 5

Raise $- 1$ to the power of $5$ .

$64 \cdot - 1 a^{2} {(a^{3})}^{5}$

Step 6

Multiply $64$ by $- 1$ .

$- 64 a^{2} {(a^{3})}^{5}$

Step 7

Multiply the exponents in ${(a^{3})}^{5}$ .

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Step 7.1

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

$- 64 a^{2} a^{3 \cdot 5}$

Step 7.2

Multiply $3$ by $5$ .

$- 64 a^{2} a^{15}$

Step 8

Multiply $a^{2}$ by $a^{15}$ by adding the exponents.

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Step 8.1

Move $a^{15}$ .

$- 64 (a^{15} a^{2})$

Step 8.2

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

$- 64 a^{15 + 2}$

Step 8.3

Add $15$ and $2$ .

$- 64 a^{17}$