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Question

If, x=(45)30÷ (45)28 and y=(45)2×(45)3, find the value of (x3÷y)2


A

1625

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B

625

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C

1625

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D

616

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Solution

The correct option is C

1625


We have:
x=(45)30÷ (45)28
x=(45)(3028) am÷an=a(mn)
x=(45)2
And,
y=(45)2×(45)3
y=(45)(2+3) am×an=a(m+n)
y=(45)5

Now,
x=(45)2, y=(45)5
x3=(45)(2×3) (am)n=a(m×n)
x3=(45)6

So, x3÷y=(45)6÷(45)5(45)(65)=45 am÷an=a(mn)

(x3÷y)2=(45)2=1625


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