Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Apply the product rule to $- x$ .

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

Step 2

Raise $- 1$ to the power of $2$ .

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

Step 3

Multiply $x^{2}$ by $1$ .

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

Step 4

Multiply the exponents in ${(y^{5})}^{2}$ .

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Step 4.1

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

$x^{2} y^{5 \cdot 2}$

Step 4.2

Multiply $5$ by $2$ .

$x^{2} y^{10}$