Question

Find the value of m if [{1/7^2}^-2]^-1/3×1/4 =7m

Answer 1

Answer: -1/3

Step-by-step explanation:

[{(1/(7)^2)^-2}^-1/3]^1/4 = 7ⁿ

(1/7)^1/3 = 7ⁿ (cancelling out exponents)

7^-1/3 = 7ⁿ

(Since bases are same, exponents are equal)

Therefore,

-1/3 = ⁿ

Answer 2

Answer:

The value is $m=-1/3$.

Step-by-step explanation:

It is given that the equation is [{(1/(7)^2)^-2}^-1/3]^1/4 = 7ⁿ

The exponents will be cancelled out.

We are left with $(\frac{1}{7} )^{1/3} =7^{m}$

Also,

$7^{-1/3}=7^{m}$

Bases are same, powers will be equated,

$m=-1/3$.

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