Question 51

In the following question, fill in the blanks to make the statements true.

By multiplying ${(\frac{5}{3})}^{4}$ by ___ we get $5^{4}$ .

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Solution

Let x be multiplied with ${(\frac{5}{3})}^{4}$ to get $5^{4} .$
So, ${(\frac{5}{3})}^{4} \times x = 5^{4}$

$∴ x = \frac{5^{4}}{{(\frac{5}{3})}^{4}} = 5^{4} \times 3^{4} \times 5^{- 4} = (5)^{4 - 4} \times 3^{4} [a^{m} \times a^{n} = a^{m + n}]$

$= 5^{0} \times 3^{4} = 3^{4}$

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