Algebra Examples

${(\frac{4}{3} x^{2} y^{3})}^{3} {(\frac{3}{16 x^{5}})}^{2}$

Step 1

Multiply $\frac{4}{3} (x^{2} y^{3})$ .

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Step 1.1

Combine $x^{2}$ and $\frac{4}{3}$ .

${(\frac{x^{2} \cdot 4}{3} y^{3})}^{3} {(\frac{3}{16 x^{5}})}^{2}$

Step 1.2

Combine $\frac{x^{2} \cdot 4}{3}$ and $y^{3}$ .

${(\frac{x^{2} \cdot 4 y^{3}}{3})}^{3} {(\frac{3}{16 x^{5}})}^{2}$

Step 2

Move $4$ to the left of $x^{2}$ .

${(\frac{4 \cdot x^{2} y^{3}}{3})}^{3} {(\frac{3}{16 x^{5}})}^{2}$

Step 3

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

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Step 3.1

Apply the product rule to $\frac{4 x^{2} y^{3}}{3}$ .

$\frac{{(4 x^{2} y^{3})}^{3}}{3^{3}} {(\frac{3}{16 x^{5}})}^{2}$

Step 3.2

Apply the product rule to $4 x^{2} y^{3}$ .

$\frac{{(4 x^{2})}^{3} {(y^{3})}^{3}}{3^{3}} {(\frac{3}{16 x^{5}})}^{2}$

Step 3.3

Apply the product rule to $4 x^{2}$ .

$\frac{4^{3} {(x^{2})}^{3} {(y^{3})}^{3}}{3^{3}} {(\frac{3}{16 x^{5}})}^{2}$

Step 4

Simplify the numerator.

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Step 4.1

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

$\frac{64 {(x^{2})}^{3} {(y^{3})}^{3}}{3^{3}} {(\frac{3}{16 x^{5}})}^{2}$

Step 4.2

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

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Step 4.2.1

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

$\frac{64 x^{2 \cdot 3} {(y^{3})}^{3}}{3^{3}} {(\frac{3}{16 x^{5}})}^{2}$

Step 4.2.2

Multiply $2$ by $3$ .

$\frac{64 x^{6} {(y^{3})}^{3}}{3^{3}} {(\frac{3}{16 x^{5}})}^{2}$

Step 4.3

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

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Step 4.3.1

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

$\frac{64 x^{6} y^{3 \cdot 3}}{3^{3}} {(\frac{3}{16 x^{5}})}^{2}$

Step 4.3.2

Multiply $3$ by $3$ .

$\frac{64 x^{6} y^{9}}{3^{3}} {(\frac{3}{16 x^{5}})}^{2}$

Step 5

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

$\frac{64 x^{6} y^{9}}{27} {(\frac{3}{16 x^{5}})}^{2}$

Step 6

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

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Step 6.1

Apply the product rule to $\frac{3}{16 x^{5}}$ .

$\frac{64 x^{6} y^{9}}{27} \cdot \frac{3^{2}}{{(16 x^{5})}^{2}}$

Step 6.2

Apply the product rule to $16 x^{5}$ .

$\frac{64 x^{6} y^{9}}{27} \cdot \frac{3^{2}}{16^{2} {(x^{5})}^{2}}$

Step 7

Combine.

$\frac{64 x^{6} y^{9} \cdot 3^{2}}{27 (16^{2} {(x^{5})}^{2})}$

Step 8

Simplify the numerator.

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Step 8.1

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

$\frac{64 x^{6} y^{9} \cdot 9}{27 \cdot 16^{2} {(x^{5})}^{2}}$

Step 8.2

Multiply $9$ by $64$ .

$\frac{576 x^{6} y^{9}}{27 \cdot 16^{2} {(x^{5})}^{2}}$

Step 9

Simplify the denominator.

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Step 9.1

Raise $16$ to the power of $2$ .

$\frac{576 x^{6} y^{9}}{27 \cdot 256 {(x^{5})}^{2}}$

Step 9.2

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

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Step 9.2.1

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

$\frac{576 x^{6} y^{9}}{27 \cdot 256 x^{5 \cdot 2}}$

Step 9.2.2

Multiply $5$ by $2$ .

$\frac{576 x^{6} y^{9}}{27 \cdot 256 x^{10}}$

Step 9.3

Multiply $27$ by $256$ .

$\frac{576 x^{6} y^{9}}{6912 x^{10}}$

Step 10

Reduce the expression by cancelling the common factors.

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Step 10.1

Cancel the common factor of $576$ and $6912$ .

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Step 10.1.1

Factor $576$ out of $576 x^{6} y^{9}$ .

$\frac{576 (x^{6} y^{9})}{6912 x^{10}}$

Step 10.1.2

Cancel the common factors.

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Step 10.1.2.1

Factor $576$ out of $6912 x^{10}$ .

$\frac{576 (x^{6} y^{9})}{576 (12 x^{10})}$

Step 10.1.2.2

Cancel the common factor.

$\frac{576 (x^{6} y^{9})}{576 (12 x^{10})}$

Step 10.1.2.3

Rewrite the expression.

$\frac{x^{6} y^{9}}{12 x^{10}}$

Step 10.2

Cancel the common factor of $x^{6}$ and $x^{10}$ .

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Step 10.2.1

Factor $x^{6}$ out of $x^{6} y^{9}$ .

$\frac{x^{6} (y^{9})}{12 x^{10}}$

Step 10.2.2

Cancel the common factors.

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Step 10.2.2.1

Factor $x^{6}$ out of $12 x^{10}$ .

$\frac{x^{6} (y^{9})}{x^{6} (12 x^{4})}$

Step 10.2.2.2

Cancel the common factor.

$\frac{x^{6} y^{9}}{x^{6} (12 x^{4})}$

Step 10.2.2.3

Rewrite the expression.

$\frac{y^{9}}{12 x^{4}}$