Question 143(iii)

Use the propeties of exponents to verify that each statement is true.
$25 (5^{n - 2}) = 5^{n}$

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Solution

$25 (5^{n - 2}) = 5^{n} L H S = 25 (5^{n - 2}) = 5^{2} (5^{n} \div 5^{2}) = 5^{2} \times 5^{n} \times \frac{1}{5^{2}} [∵ a^{m} \div a^{n} = (a)^{m - n}] = 5^{2 + n - 2} = 5^{n} = R H S$

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