Question

Find the value of "K"

Answer 1

$\huge\red{Answer\: is}$

$\frac{(125) {}^{ - 3} }{(25) {}^{ \frac{1}{4} } } = 5 {}^{k} \\ \frac{5 {}^{3 \times ( - 3)} }{5 {}^{2 \times \frac{1}{4} } } = 5 {}^{k} \\ 5 {}^{ - 9- \frac{1}{2} } = 5 {}^{k} \\ 5 {}^{ \frac{ - 19}{2} } = 5 {}^{k} \\ \frac{ - 19}{2} = k$
Hope it helps you

Answer 2

(5^3)^-3 ÷ (5^2)^1/4 = 5^k
=> 5^-9 ÷ 5^1/2 = 5^k
=> 5^ -9-1/2 = 5^k
=> 5^ -19/2 = 5^k
so , k = -19/2