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Question

If x=(25)30÷(52)28 and y=(25)2×(25)3, then find the value of (x3÷y)2.

A
25
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B
254
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C
540
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D
425
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Solution

The correct option is D 425

Given, x=(25)30÷(52)28 and y=(25)2×(25)3

x=(25)30÷(52)28

=(25)30÷(25)28[(a)m=1am]

= (25)3028 [aman = amn]

= (25)2

x3= [(25)2]3

i.e., x3=(25)6 (i)

[(am)n = amn]

y=(25)2×(25)3

y=(25)2+3 [am×an = am+n]

i.e., y=(25)5 (ii)

From (i) and (ii),x3÷y=(25)6(25)5

=(25)65 [aman = amn]

=25

(x3÷y)2=425


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