Algebra Examples

$\frac{32 x^{35} y^{15}}{8 x^{2} y^{5}} \cdot {(4 x y)}^{2}$

Step 1

Cancel the common factor of $32$ and $8$ .

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Step 1.1

Factor $8$ out of $32 x^{35} y^{15}$ .

$\frac{8 (4 x^{35} y^{15})}{8 x^{2} y^{5}} \cdot {(4 x y)}^{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $8$ out of $8 x^{2} y^{5}$ .

$\frac{8 (4 x^{35} y^{15})}{8 (x^{2} y^{5})} \cdot {(4 x y)}^{2}$

Step 1.2.2

Cancel the common factor.

$\frac{8 (4 x^{35} y^{15})}{8 (x^{2} y^{5})} \cdot {(4 x y)}^{2}$

Step 1.2.3

Rewrite the expression.

$\frac{4 x^{35} y^{15}}{x^{2} y^{5}} \cdot {(4 x y)}^{2}$

Step 2

Cancel the common factor of $x^{35}$ and $x^{2}$ .

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Step 2.1

Factor $x^{2}$ out of $4 x^{35} y^{15}$ .

$\frac{x^{2} (4 x^{33} y^{15})}{x^{2} y^{5}} \cdot {(4 x y)}^{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x^{2}$ out of $x^{2} y^{5}$ .

$\frac{x^{2} (4 x^{33} y^{15})}{x^{2} (y^{5})} \cdot {(4 x y)}^{2}$

Step 2.2.2

Cancel the common factor.

$\frac{x^{2} (4 x^{33} y^{15})}{x^{2} y^{5}} \cdot {(4 x y)}^{2}$

Step 2.2.3

Rewrite the expression.

$\frac{4 x^{33} y^{15}}{y^{5}} \cdot {(4 x y)}^{2}$

Step 3

Cancel the common factor of $y^{15}$ and $y^{5}$ .

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Step 3.1

Factor $y^{5}$ out of $4 x^{33} y^{15}$ .

$\frac{y^{5} (4 x^{33} y^{10})}{y^{5}} \cdot {(4 x y)}^{2}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{y^{5} (4 x^{33} y^{10})}{y^{5} \cdot 1} \cdot {(4 x y)}^{2}$

Step 3.2.2

Cancel the common factor.

$\frac{y^{5} (4 x^{33} y^{10})}{y^{5} \cdot 1} \cdot {(4 x y)}^{2}$

Step 3.2.3

Rewrite the expression.

$\frac{4 x^{33} y^{10}}{1} \cdot {(4 x y)}^{2}$

Step 3.2.4

Divide $4 x^{33} y^{10}$ by $1$ .

$4 x^{33} y^{10} \cdot {(4 x y)}^{2}$

Step 4

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

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Step 4.1

Apply the product rule to $4 x y$ .

$4 x^{33} y^{10} \cdot ({(4 x)}^{2} y^{2})$

Step 4.2

Apply the product rule to $4 x$ .

$4 x^{33} y^{10} \cdot (4^{2} x^{2} y^{2})$

Step 5

Multiply $4$ by $4^{2}$ by adding the exponents.

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Step 5.1

Move $4^{2}$ .

$4^{2} \cdot 4 x^{33} y^{10} \cdot (x^{2} y^{2})$

Step 5.2

Multiply $4^{2}$ by $4$ .

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Step 5.2.1

Raise $4$ to the power of $1$ .

$4^{2} \cdot 4^{1} x^{33} y^{10} \cdot (x^{2} y^{2})$

Step 5.2.2

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

$4^{2 + 1} x^{33} y^{10} \cdot (x^{2} y^{2})$

Step 5.3

Add $2$ and $1$ .

$4^{3} x^{33} y^{10} \cdot (x^{2} y^{2})$

Step 6

Multiply $x^{33}$ by $x^{2}$ by adding the exponents.

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Step 6.1

Move $x^{2}$ .

$4^{3} (x^{2} x^{33}) y^{10} \cdot y^{2}$

Step 6.2

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

$4^{3} x^{2 + 33} y^{10} \cdot y^{2}$

Step 6.3

Add $2$ and $33$ .

$4^{3} x^{35} y^{10} \cdot y^{2}$

Step 7

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

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Step 7.1

Move $y^{2}$ .

$4^{3} x^{35} (y^{2} y^{10})$

Step 7.2

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

$4^{3} x^{35} y^{2 + 10}$

Step 7.3

Add $2$ and $10$ .

$4^{3} x^{35} y^{12}$

Step 8

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

$64 x^{35} y^{12}$