Algebra Examples

${(3 y^{\frac{2}{3}})}^{3} {(2 y^{2})}^{2}$

Step 1

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

$3^{3} {(y^{\frac{2}{3}})}^{3} {(2 y^{2})}^{2}$

Step 2

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

$27 {(y^{\frac{2}{3}})}^{3} {(2 y^{2})}^{2}$

Step 3

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

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Step 3.1

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

$27 y^{\frac{2}{3} \cdot 3} {(2 y^{2})}^{2}$

Step 3.2

Cancel the common factor of $3$ .

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Step 3.2.1

Cancel the common factor.

$27 y^{\frac{2}{3} \cdot 3} {(2 y^{2})}^{2}$

Step 3.2.2

Rewrite the expression.

$27 y^{2} {(2 y^{2})}^{2}$

Step 4

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

$27 y^{2} (2^{2} {(y^{2})}^{2})$

Step 5

Rewrite using the commutative property of multiplication.

$27 \cdot 2^{2} y^{2} {(y^{2})}^{2}$

Step 6

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

$27 \cdot 4 y^{2} {(y^{2})}^{2}$

Step 7

Multiply $27$ by $4$ .

$108 y^{2} {(y^{2})}^{2}$

Step 8

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

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Step 8.1

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

$108 y^{2} y^{2 \cdot 2}$

Step 8.2

Multiply $2$ by $2$ .

$108 y^{2} y^{4}$

Step 9

Multiply $y^{2}$ by $y^{4}$ by adding the exponents.

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Step 9.1

Move $y^{4}$ .

$108 (y^{4} y^{2})$

Step 9.2

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

$108 y^{4 + 2}$

Step 9.3

Add $4$ and $2$ .

$108 y^{6}$