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Question
By multiplying `(5/3)^4` by ______ we get 54.
Fill in the Blanks
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Solution
By multiplying `(5/3)^4` by 81 we get 54.
Explanation:
Let x be multiplied with `(5/3)^4` to get 54.
So, `(5/3)^4 xx x = 5^4`
∴ `x = 5^4/(5/3)^4 = 5^4 xx 3^4 xx 5^-4`
= (5)4 – 4 × 34 ...`[∵ a^-m = 1/a^m, a^m xx a^n = (a)^(m + n)]`
= 50 × 34
= 1 × 81
= 81
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