Pre-Algebra Examples

${(3 x^{4})}^{9} \div {(3^{5} x^{6})}^{3}$

Step 1

Rewrite the division as a fraction.

$\frac{{(3 x^{4})}^{9}}{{(3^{5} x^{6})}^{3}}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{3^{9} {(x^{4})}^{9}}{{(3^{5} x^{6})}^{3}}$

Step 2.2

Raise $3$ to the power of $9$ .

$\frac{19683 {(x^{4})}^{9}}{{(3^{5} x^{6})}^{3}}$

Step 2.3

Multiply the exponents in ${(x^{4})}^{9}$ .

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Step 2.3.1

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

$\frac{19683 x^{4 \cdot 9}}{{(3^{5} x^{6})}^{3}}$

Step 2.3.2

Multiply $4$ by $9$ .

$\frac{19683 x^{36}}{{(3^{5} x^{6})}^{3}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $3^{5} x^{6}$ .

$\frac{19683 x^{36}}{{(3^{5})}^{3} {(x^{6})}^{3}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{19683 x^{36}}{3^{5 \cdot 3} {(x^{6})}^{3}}$

Step 3.2.2

Multiply $5$ by $3$ .

$\frac{19683 x^{36}}{3^{15} {(x^{6})}^{3}}$

Step 3.3

Raise $3$ to the power of $15$ .

$\frac{19683 x^{36}}{14348907 {(x^{6})}^{3}}$

Step 3.4

Multiply the exponents in ${(x^{6})}^{3}$ .

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Step 3.4.1

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

$\frac{19683 x^{36}}{14348907 x^{6 \cdot 3}}$

Step 3.4.2

Multiply $6$ by $3$ .

$\frac{19683 x^{36}}{14348907 x^{18}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $19683$ and $14348907$ .

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Step 4.1.1

Factor $19683$ out of $19683 x^{36}$ .

$\frac{19683 (x^{36})}{14348907 x^{18}}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $19683$ out of $14348907 x^{18}$ .

$\frac{19683 (x^{36})}{19683 (729 x^{18})}$

Step 4.1.2.2

Cancel the common factor.

$\frac{19683 x^{36}}{19683 (729 x^{18})}$

Step 4.1.2.3

Rewrite the expression.

$\frac{x^{36}}{729 x^{18}}$

Step 4.2

Cancel the common factor of $x^{36}$ and $x^{18}$ .

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Step 4.2.1

Factor $x^{18}$ out of $x^{36}$ .

$\frac{x^{18} x^{18}}{729 x^{18}}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Factor $x^{18}$ out of $729 x^{18}$ .

$\frac{x^{18} x^{18}}{x^{18} \cdot 729}$

Step 4.2.2.2

Cancel the common factor.

$\frac{x^{18} x^{18}}{x^{18} \cdot 729}$

Step 4.2.2.3

Rewrite the expression.

$\frac{x^{18}}{729}$