Algebra Examples

${(3 x^{3} y)}^{4} - {(7 x^{5} y)}^{2} \cdot x^{2} y^{2}$

Step 1

Simplify each term.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

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

${(3 x^{3})}^{4} y^{4} - {(7 x^{5} y)}^{2} \cdot (x^{2} y^{2})$

Step 1.1.2

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

$3^{4} {(x^{3})}^{4} y^{4} - {(7 x^{5} y)}^{2} \cdot (x^{2} y^{2})$

Step 1.2

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

$81 {(x^{3})}^{4} y^{4} - {(7 x^{5} y)}^{2} \cdot (x^{2} y^{2})$

Step 1.3

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

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Step 1.3.1

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

$81 x^{3 \cdot 4} y^{4} - {(7 x^{5} y)}^{2} \cdot (x^{2} y^{2})$

Step 1.3.2

Multiply $3$ by $4$ .

$81 x^{12} y^{4} - {(7 x^{5} y)}^{2} \cdot (x^{2} y^{2})$

Step 1.4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.4.1

Apply the product rule to $7 x^{5} y$ .

$81 x^{12} y^{4} - ({(7 x^{5})}^{2} y^{2}) \cdot (x^{2} y^{2})$

Step 1.4.2

Apply the product rule to $7 x^{5}$ .

$81 x^{12} y^{4} - (7^{2} {(x^{5})}^{2} y^{2}) \cdot (x^{2} y^{2})$

Step 1.5

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

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Step 1.5.1

Move $y^{2}$ .

$81 x^{12} y^{4} - (7^{2} {(x^{5})}^{2} (y^{2} y^{2})) \cdot x^{2}$

Step 1.5.2

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

$81 x^{12} y^{4} - (7^{2} {(x^{5})}^{2} y^{2 + 2}) \cdot x^{2}$

Step 1.5.3

Add $2$ and $2$ .

$81 x^{12} y^{4} - (7^{2} {(x^{5})}^{2} y^{4}) \cdot x^{2}$

Step 1.6

Raise $7$ to the power of $2$ .

$81 x^{12} y^{4} - (49 {(x^{5})}^{2} y^{4}) \cdot x^{2}$

Step 1.7

Multiply the exponents in ${(x^{5})}^{2}$ .

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Step 1.7.1

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

$81 x^{12} y^{4} - (49 x^{5 \cdot 2} y^{4}) \cdot x^{2}$

Step 1.7.2

Multiply $5$ by $2$ .

$81 x^{12} y^{4} - (49 x^{10} y^{4}) \cdot x^{2}$

Step 1.8

Multiply $x^{10}$ by $x^{2}$ by adding the exponents.

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Step 1.8.1

Move $x^{2}$ .

$81 x^{12} y^{4} - (49 (x^{2} x^{10}) y^{4})$

Step 1.8.2

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

$81 x^{12} y^{4} - (49 x^{2 + 10} y^{4})$

Step 1.8.3

Add $2$ and $10$ .

$81 x^{12} y^{4} - (49 x^{12} y^{4})$

Step 1.9

Multiply $49$ by $- 1$ .

$81 x^{12} y^{4} - 49 x^{12} y^{4}$

Step 2

Subtract $49 x^{12} y^{4}$ from $81 x^{12} y^{4}$ .

$32 x^{12} y^{4}$