Precalculus Examples

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

Step 1

Apply the product rule to $2 y^{4}$ .

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

Step 2

Rewrite using the commutative property of multiplication.

$6 \cdot 2^{2} y^{2} {(y^{4})}^{2}$

Step 3

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

$6 \cdot 4 y^{2} {(y^{4})}^{2}$

Step 4

Multiply $6$ by $4$ .

$24 y^{2} {(y^{4})}^{2}$

Step 5

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

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Step 5.1

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

$24 y^{2} y^{4 \cdot 2}$

Step 5.2

Multiply $4$ by $2$ .

$24 y^{2} y^{8}$

Step 6

Multiply $y^{2}$ by $y^{8}$ by adding the exponents.

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Step 6.1

Move $y^{8}$ .

$24 (y^{8} y^{2})$

Step 6.2

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

$24 y^{8 + 2}$

Step 6.3

Add $8$ and $2$ .

$24 y^{10}$