Basic Math Examples

${(x^{2} y^{3} z^{4})}^{2}$

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 $x^{2} y^{3} z^{4}$ .

${(x^{2} y^{3})}^{2} {(z^{4})}^{2}$

Step 1.2

Apply the product rule to $x^{2} y^{3}$ .

${(x^{2})}^{2} {(y^{3})}^{2} {(z^{4})}^{2}$

Step 2

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

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Step 2.1

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

$x^{2 \cdot 2} {(y^{3})}^{2} {(z^{4})}^{2}$

Step 2.2

Multiply $2$ by $2$ .

$x^{4} {(y^{3})}^{2} {(z^{4})}^{2}$

Step 3

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

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Step 3.1

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

$x^{4} y^{3 \cdot 2} {(z^{4})}^{2}$

Step 3.2

Multiply $3$ by $2$ .

$x^{4} y^{6} {(z^{4})}^{2}$

Step 4

Multiply the exponents in ${(z^{4})}^{2}$ .

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Step 4.1

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

$x^{4} y^{6} z^{4 \cdot 2}$

Step 4.2

Multiply $4$ by $2$ .

$x^{4} y^{6} z^{8}$