Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Multiply $3$ by $2$ .

${(- 2 x y^{2})}^{6}$

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 $- 2 x y^{2}$ .

${(- 2 x)}^{6} {(y^{2})}^{6}$

Step 2.2

Apply the product rule to $- 2 x$ .

${(- 2)}^{6} x^{6} {(y^{2})}^{6}$

Step 3

Raise $- 2$ to the power of $6$ .

$64 x^{6} {(y^{2})}^{6}$

Step 4

Multiply the exponents in ${(y^{2})}^{6}$ .

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Step 4.1

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

$64 x^{6} y^{2 \cdot 6}$

Step 4.2

Multiply $2$ by $6$ .

$64 x^{6} y^{12}$