(25)^4 can be written as (5× 5)^4 =(5^2)^4 (5^2)^4 can be written as (5)^2× 4 ... [∵ (a^m)^n=a^mn] =5^8 Then, =5^8÷ 5^3 =5^8 3 ...[∵ a^m÷ a^n=a^m n] =5^5 ...

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Byju's Answer

Standard VII

Mathematics

Zero Exponent

Solve : 254÷ ...

Question

Solve : $25^{4} \div 5^{3}$

None of the above

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5^{5}

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Solution

The correct option is B $5^{5}$
$(25)^{4}$ can be written as $(5 \times 5)^{4}$

$= (5^{2})^{4}$

$(5^{2})^{4}$ can be written as $(5)^{2 \times 4} . . . [∵ (a^{m})^{n} = a^{m n}]$

$= 5^{8}$

Then,

$= 5^{8} \div 5^{3}$

$= 5^{8 - 3} . . . [∵ a^{m} \div a^{n} = a^{m - n}]$

$= 5^{5}$

Suggest Corrections

Solve : 254÷53

The correct option is B 55(25)4 can be written as (5×5)4 =(52)4 (52)4 can be written as (5)2×4...[∵(am)n=amn] =58 Then, =58÷53 =58−3...[∵am÷an=am−n] =55

Solve : $25^{4} \div 5^{3}$

The correct option is B $5^{5}$
$(25)^{4}$ can be written as $(5 \times 5)^{4}$

$= (5^{2})^{4}$

$(5^{2})^{4}$ can be written as $(5)^{2 \times 4} . . . [∵ (a^{m})^{n} = a^{m n}]$

$= 5^{8}$

Then,

$= 5^{8} \div 5^{3}$

$= 5^{8 - 3} . . . [∵ a^{m} \div a^{n} = a^{m - n}]$

$= 5^{5}$