Algebra Examples

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

Step 1

Rewrite $- 1 x^{5}$ as $- x^{5}$ .

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

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 $- x^{5} y^{3}$ .

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

Step 2.2

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

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

Step 3

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

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

Step 4

Multiply ${(x^{5})}^{2}$ by $1$ .

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Multiply $5$ by $2$ .

$x^{10} {(y^{3})}^{2}$

Step 6

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

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Step 6.1

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

$x^{10} y^{3 \cdot 2}$

Step 6.2

Multiply $3$ by $2$ .

$x^{10} y^{6}$