Pre-Algebra Examples

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

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 $3 x^{4} y$ .

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

Step 1.2

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

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

Step 2

Raise $3$ to the power of $2$ .

$5 (9 {(x^{4})}^{2} y^{2}) {(x y^{3})}^{4}$

Step 3

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

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Step 3.1

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

$5 (9 x^{4 \cdot 2} y^{2}) {(x y^{3})}^{4}$

Step 3.2

Multiply $4$ by $2$ .

$5 (9 x^{8} y^{2}) {(x y^{3})}^{4}$

Step 4

Multiply $9$ by $5$ .

$45 (x^{8} y^{2}) {(x y^{3})}^{4}$

Step 5

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

$45 x^{8} y^{2} (x^{4} {(y^{3})}^{4})$

Step 6

Multiply $x^{8}$ by $x^{4}$ by adding the exponents.

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Step 6.1

Move $x^{4}$ .

$45 (x^{4} x^{8}) y^{2} {(y^{3})}^{4}$

Step 6.2

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

$45 x^{4 + 8} y^{2} {(y^{3})}^{4}$

Step 6.3

Add $4$ and $8$ .

$45 x^{12} y^{2} {(y^{3})}^{4}$

Step 7

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

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Step 7.1

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

$45 x^{12} y^{2} y^{3 \cdot 4}$

Step 7.2

Multiply $3$ by $4$ .

$45 x^{12} y^{2} y^{12}$

Step 8

Multiply $y^{2}$ by $y^{12}$ by adding the exponents.

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Step 8.1

Move $y^{12}$ .

$45 x^{12} (y^{12} y^{2})$

Step 8.2

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

$45 x^{12} y^{12 + 2}$

Step 8.3

Add $12$ and $2$ .

$45 x^{12} y^{14}$