Basic Math Examples

$\frac{| {({(- a)}^{3})}^{5} \cdot {(- a)}^{2} |}{a^{5}}$

Step 1

Apply the product rule to $- a$ .

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

Step 2

Apply the product rule to ${(- 1)}^{3} a^{3}$ .

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

Step 3

Apply the product rule to $- a$ .

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

Step 4

Multiply the exponents in ${({(- 1)}^{3})}^{5}$ .

Tap for more steps...

Step 4.1

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

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

Step 4.2

Multiply $3$ by $5$ .

$\frac{| {(- 1)}^{15} {(a^{3})}^{5} \cdot {(- 1)}^{2} a^{2} |}{a^{5}}$

Step 5

Multiply ${(- 1)}^{15}$ by ${(- 1)}^{2}$ by adding the exponents.

Tap for more steps...

Step 5.1

Move ${(- 1)}^{2}$ .

$\frac{| {(- 1)}^{2} {(- 1)}^{15} {(a^{3})}^{5} a^{2} |}{a^{5}}$

Step 5.2

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

$\frac{| {(- 1)}^{2 + 15} {(a^{3})}^{5} a^{2} |}{a^{5}}$

Step 5.3

Add $2$ and $15$ .

$\frac{| {(- 1)}^{17} {(a^{3})}^{5} a^{2} |}{a^{5}}$

Step 6

Raise $- 1$ to the power of $17$ .

$\frac{| - {(a^{3})}^{5} a^{2} |}{a^{5}}$

Step 7

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

Tap for more steps...

Step 7.1

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

$\frac{| - a^{3 \cdot 5} a^{2} |}{a^{5}}$

Step 7.2

Multiply $3$ by $5$ .

$\frac{| - a^{15} a^{2} |}{a^{5}}$

Step 8

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

Tap for more steps...

Step 8.1

Move $a^{2}$ .

$\frac{| - (a^{2} a^{15}) |}{a^{5}}$

Step 8.2

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

$\frac{| - a^{2 + 15} |}{a^{5}}$

Step 8.3

Add $2$ and $15$ .

$\frac{| - a^{17} |}{a^{5}}$

Step 9

Remove non-negative terms from the absolute value.

$\frac{| a^{17} |}{a^{5}}$