Pre-Algebra Examples

${(5 x y^{4})}^{3} \cdot (x^{2} y)$

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 $5 x y^{4}$ .

${(5 x)}^{3} {(y^{4})}^{3} \cdot (x^{2} y)$

Step 1.2

Apply the product rule to $5 x$ .

$5^{3} x^{3} {(y^{4})}^{3} \cdot (x^{2} y)$

Step 2

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

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Step 2.1

Move $x^{2}$ .

$5^{3} (x^{2} x^{3}) {(y^{4})}^{3} \cdot y$

Step 2.2

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

$5^{3} x^{2 + 3} {(y^{4})}^{3} \cdot y$

Step 2.3

Add $2$ and $3$ .

$5^{3} x^{5} {(y^{4})}^{3} \cdot y$

Step 3

Raise $5$ to the power of $3$ .

$125 x^{5} {(y^{4})}^{3} \cdot y$

Step 4

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

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Step 4.1

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

$125 x^{5} y^{4 \cdot 3} \cdot y$

Step 4.2

Multiply $4$ by $3$ .

$125 x^{5} y^{12} \cdot y$

Step 5

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

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Step 5.1

Move $y$ .

$125 x^{5} (y \cdot y^{12})$

Step 5.2

Multiply $y$ by $y^{12}$ .

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Step 5.2.1

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

$125 x^{5} (y^{1} y^{12})$

Step 5.2.2

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

$125 x^{5} y^{1 + 12}$

Step 5.3

Add $1$ and $12$ .

$125 x^{5} y^{13}$