Algebra Examples

${(5^{3})}^{9} \div 5^{12}$

Step 1

Rewrite the division as a fraction.

$\frac{{(5^{3})}^{9}}{5^{12}}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply the exponents in ${(5^{3})}^{9}$ .

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Step 2.1.1

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

$\frac{5^{3 \cdot 9}}{5^{12}}$

Step 2.1.2

Multiply $3$ by $9$ .

$\frac{5^{27}}{5^{12}}$

Step 2.2

Raise $5$ to the power of $27$ .

$\frac{7450580596923830000}{5^{12}}$

Step 3

Raise $5$ to the power of $12$ .

$\frac{7450580596923830000}{244140625}$

Step 4

Cancel the common factor of $7450580596923830000$ and $244140625$ .

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Step 4.1

Factor $625$ out of $7450580596923830000$ .

$\frac{625 (11920928955078128)}{244140625}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $625$ out of $244140625$ .

$\frac{625 \cdot 11920928955078128}{625 \cdot 390625}$

Step 4.2.2

Cancel the common factor.

$\frac{625 \cdot 11920928955078128}{625 \cdot 390625}$

Step 4.2.3

Rewrite the expression.

$\frac{11920928955078128}{390625}$