Algebra Examples

${(- 2 x^{2})}^{3} {(- y)}^{5}$

Step 1

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

${(- 2)}^{3} {(x^{2})}^{3} {(- y)}^{5}$

Step 2

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

$- 8 {(x^{2})}^{3} {(- y)}^{5}$

Step 3

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 3.1

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

$- 8 x^{2 \cdot 3} {(- y)}^{5}$

Step 3.2

Multiply $2$ by $3$ .

$- 8 x^{6} {(- y)}^{5}$

Step 4

Apply the product rule to $- y$ .

$- 8 x^{6} ({(- 1)}^{5} y^{5})$

Step 5

Rewrite using the commutative property of multiplication.

$- 8 \cdot {(- 1)}^{5} x^{6} y^{5}$

Step 6

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

$- 8 \cdot - 1 x^{6} y^{5}$

Step 7

Multiply $- 8$ by $- 1$ .

$8 x^{6} y^{5}$