Question

in each of the following , find the value of x​

Answer 1

Answer:

(i) -2

(iv) $\frac{2}{3}$

Step-by-step explanation:

(i) $\frac{a^{-3}\times b^{-4}}{a^{-2}\times b^{-3}}$ = (ab)ˣ

$\frac{ab^{-3+-4}}{ab^{-2+-3}}$ = (ab)ˣ

$\frac{ab^{-3-4}}{ab^{-2-3}}$ = (ab)ˣ

$\frac{ab^{-7}}{ab^{-5}}$ = (ab)ˣ

ab⁻⁷⁻⁻⁵ = (ab)ˣ

ab⁻⁷⁺⁵ = (ab)ˣ

ab⁻² = (ab)ˣ

(ab)ˣ = ab⁻²

x = -2

(iv) $(\frac{1}{3})^{-2}$ + $(\frac{1}{4})^{-2}$ = (125)ˣ

3² + 4² = (125)ˣ

9 + 16 = (125)ˣ

25 = (125)ˣ

(125)ˣ = 25

$5^{3^x}$ = 5²

5³ˣ = 5²

3x = 2

x = $\frac{2}{3}$

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