Pre-Algebra Examples

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

Step 1

Apply the product rule to $x^{5} y^{3}$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Multiply $5$ by $2$ .

$x^{10} {(y^{3})}^{2} {(x^{3} y^{2})}^{5}$

Step 3

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

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Step 3.1

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

$x^{10} y^{3 \cdot 2} {(x^{3} y^{2})}^{5}$

Step 3.2

Multiply $3$ by $2$ .

$x^{10} y^{6} {(x^{3} y^{2})}^{5}$

Step 4

Apply the product rule to $x^{3} y^{2}$ .

$x^{10} y^{6} ({(x^{3})}^{5} {(y^{2})}^{5})$

Step 5

Multiply the exponents in ${(x^{3})}^{5}$ .

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Step 5.1

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

$x^{10} y^{6} (x^{3 \cdot 5} {(y^{2})}^{5})$

Step 5.2

Multiply $3$ by $5$ .

$x^{10} y^{6} (x^{15} {(y^{2})}^{5})$

Step 6

Multiply $x^{10}$ by $x^{15}$ by adding the exponents.

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Step 6.1

Move $x^{15}$ .

$x^{15} x^{10} y^{6} {(y^{2})}^{5}$

Step 6.2

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

$x^{15 + 10} y^{6} {(y^{2})}^{5}$

Step 6.3

Add $15$ and $10$ .

$x^{25} y^{6} {(y^{2})}^{5}$

Step 7

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

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Step 7.1

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

$x^{25} y^{6} y^{2 \cdot 5}$

Step 7.2

Multiply $2$ by $5$ .

$x^{25} y^{6} y^{10}$

Step 8

Multiply $y^{6}$ by $y^{10}$ by adding the exponents.

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Step 8.1

Move $y^{10}$ .

$x^{25} (y^{10} y^{6})$

Step 8.2

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

$x^{25} y^{10 + 6}$

Step 8.3

Add $10$ and $6$ .

$x^{25} y^{16}$