Question

25 power 4 divided by 5 power 3

Answer 1

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Answer 2

$\displaystyle \sf{ \frac{ {25}^{4} }{ {5}^{3} } = {5}^{5} = 3125 }$

Given :

$\displaystyle \sf{ \frac{ {25}^{4} }{ {5}^{3} } }$

To find :

The value of the expression

Formula :

We are aware of the formula on indices that :

‌$\sf{1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n} }$

‌$\displaystyle \sf{2. \: \: \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

‌$\displaystyle \sf{3. \: \: \: { ({a}^{m} )}^{n} = {a}^{mn} }$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ \frac{ {25}^{4} }{ {5}^{3} } }$

Step 2 of 2 :

Simplify the expression

$\displaystyle \sf{ \frac{ {25}^{4} }{ {5}^{3} } }$

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

$\displaystyle \sf{ = \frac{ {5}^{2 \times 4} }{ {5}^{3} } }$

$\displaystyle \sf{ = \frac{ {5}^{8} }{ {5}^{3} } }$

$\displaystyle \sf{ ={5}^{8 - 3} }$

$\displaystyle \sf{ ={5}^{5} }$

$\displaystyle \sf{ = 3125 }$

Thus we get

$\displaystyle \sf{ \frac{ {25}^{4} }{ {5}^{3} } = {5}^{5} = 3125 }$