Algebra Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

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 $3 x y^{3}$ .

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

Step 2.2

Apply the product rule to $3 x$ .

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

Step 3

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 3.1

Move $x$ .

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

Step 3.2

Multiply $x$ by $x^{3}$ .

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Step 3.2.1

Raise $x$ to the power of $1$ .

$2 (3^{3} (x^{1} x^{3}) {(y^{3})}^{3})$

Step 3.2.2

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

$2 (3^{3} x^{1 + 3} {(y^{3})}^{3})$

Step 3.3

Add $1$ and $3$ .

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

Step 4

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

$2 (27 x^{4} {(y^{3})}^{3})$

Step 5

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

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Step 5.1

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

$2 (27 x^{4} y^{3 \cdot 3})$

Step 5.2

Multiply $3$ by $3$ .

$2 (27 x^{4} y^{9})$

Step 6

Multiply $27$ by $2$ .

$54 x^{4} y^{9}$