Algebra Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

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

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

Step 2.2

Apply the product rule to $3 x^{4}$ .

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

Step 3

Raise $3$ to the power of $4$ .

$2 (81 {(x^{4})}^{4} {(y^{3})}^{4}) {(y^{2})}^{3}$

Step 4

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

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Step 4.1

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

$2 (81 x^{4 \cdot 4} {(y^{3})}^{4}) {(y^{2})}^{3}$

Step 4.2

Multiply $4$ by $4$ .

$2 (81 x^{16} {(y^{3})}^{4}) {(y^{2})}^{3}$

Step 5

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

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Step 5.1

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

$2 (81 x^{16} y^{3 \cdot 4}) {(y^{2})}^{3}$

Step 5.2

Multiply $3$ by $4$ .

$2 (81 x^{16} y^{12}) {(y^{2})}^{3}$

Step 6

Multiply $81$ by $2$ .

$162 (x^{16} y^{12}) {(y^{2})}^{3}$

Step 7

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

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Step 7.1

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

$162 x^{16} y^{12} y^{2 \cdot 3}$

Step 7.2

Multiply $2$ by $3$ .

$162 x^{16} y^{12} y^{6}$

Step 8

Multiply $y^{12}$ by $y^{6}$ by adding the exponents.

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Step 8.1

Move $y^{6}$ .

$162 x^{16} (y^{6} y^{12})$

Step 8.2

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

$162 x^{16} y^{6 + 12}$

Step 8.3

Add $6$ and $12$ .

$162 x^{16} y^{18}$