Algebra Examples

${(- 1)}^{3} {(5 x^{2} y)}^{3}$

Step 1

Raise $- 1$ to the power of $3$ .

$- 1 {(5 x^{2} y)}^{3}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $5 x^{2} y$ .

$- 1 ({(5 x^{2})}^{3} y^{3})$

Step 2.2

Apply the product rule to $5 x^{2}$ .

$- 1 (5^{3} {(x^{2})}^{3} y^{3})$

Step 3

Raise $5$ to the power of $3$ .

$- 1 (125 {(x^{2})}^{3} y^{3})$

Step 4

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

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Step 4.1

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

$- 1 (125 x^{2 \cdot 3} y^{3})$

Step 4.2

Multiply $2$ by $3$ .

$- 1 (125 x^{6} y^{3})$

Step 5

Multiply $125$ by $- 1$ .

$- 125 x^{6} y^{3}$