Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Multiply the exponents in ${(5^{3})}^{2}$ .

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Step 1.1.1

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

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

Step 1.1.2

Multiply $3$ by $2$ .

$\frac{5^{6}}{{(5^{2})}^{4}}$

Step 1.2

Raise $5$ to the power of $6$ .

$\frac{15625}{{(5^{2})}^{4}}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply the exponents in ${(5^{2})}^{4}$ .

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Step 2.1.1

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

$\frac{15625}{5^{2 \cdot 4}}$

Step 2.1.2

Multiply $2$ by $4$ .

$\frac{15625}{5^{8}}$

Step 2.2

Raise $5$ to the power of $8$ .

$\frac{15625}{390625}$

Step 3

Cancel the common factor of $15625$ and $390625$ .

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Step 3.1

Factor $15625$ out of $15625$ .

$\frac{15625 (1)}{390625}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $15625$ out of $390625$ .

$\frac{15625 \cdot 1}{15625 \cdot 25}$

Step 3.2.2

Cancel the common factor.

$\frac{15625 \cdot 1}{15625 \cdot 25}$

Step 3.2.3

Rewrite the expression.

$\frac{1}{25}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{25}$

Decimal Form:

$0.04$