Basic Math Examples

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

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 $2 y z^{4}$ .

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

Step 1.2

Apply the product rule to $2 y$ .

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

Step 2

Raise $2$ to the power of $3$ .

$8 y^{3} {(z^{4})}^{3} z^{2}$

Step 3

Multiply the exponents in ${(z^{4})}^{3}$ .

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Step 3.1

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

$8 y^{3} z^{4 \cdot 3} z^{2}$

Step 3.2

Multiply $4$ by $3$ .

$8 y^{3} z^{12} z^{2}$

Step 4

Multiply $z^{12}$ by $z^{2}$ by adding the exponents.

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Step 4.1

Move $z^{2}$ .

$8 y^{3} (z^{2} z^{12})$

Step 4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8 y^{3} z^{2 + 12}$

Step 4.3

Add $2$ and $12$ .

$8 y^{3} z^{14}$