Basic Math Examples

$\frac{25^{4} \cdot 125^{10}}{5^{37}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $25$ as $5^{2}$ .

$\frac{{(5^{2})}^{4} \cdot 125^{10}}{5^{37}}$

Step 1.2

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

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Step 1.2.1

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

$\frac{5^{2 \cdot 4} \cdot 125^{10}}{5^{37}}$

Step 1.2.2

Multiply $2$ by $4$ .

$\frac{5^{8} \cdot 125^{10}}{5^{37}}$

Step 1.3

Rewrite $125$ as $5^{3}$ .

$\frac{5^{8} \cdot {(5^{3})}^{10}}{5^{37}}$

Step 1.4

Multiply the exponents in ${(5^{3})}^{10}$ .

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Step 1.4.1

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

$\frac{5^{8} \cdot 5^{3 \cdot 10}}{5^{37}}$

Step 1.4.2

Multiply $3$ by $10$ .

$\frac{5^{8} \cdot 5^{30}}{5^{37}}$

Step 1.5

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

$\frac{5^{8 + 30}}{5^{37}}$

Step 1.6

Add $8$ and $30$ .

$\frac{5^{38}}{5^{37}}$

Step 2

Simplify the expression.

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Step 2.1

Raise $5$ to the power of $37$ .

$\frac{5^{38}}{72759576141834200000000000}$

Step 2.2

Raise $5$ to the power of $38$ .

$\frac{363797880709171000000000000}{72759576141834200000000000}$

Step 2.3

Divide $363797880709171000000000000$ by $72759576141834200000000000$ .

$5$