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CTET Paper II (Mathematics and Science) 3 Jan 2022 Solved Paper

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Question : 32 of 150

Marks: +1, -0

If

(\frac{2}{7})^{-3}X(\frac{4}{49})^{6}=(\frac{2}{7})^{2m-1}

, then what is the value of m?

4
5
$-4$
$-5$

Solution:

Concept:

Laws of exponents:

(a^m)^n = a^{mn}

,

a^m \times a^n = a^{m+n}

, and if

a^m = a^n

, then

m = n

.

Explanation:

First, rewrite

\frac{4}{49}

as

(\frac{2}{7})^2

because

4=2^2

and

49=7^2

.

So

(\frac{4}{49})^6 = \left((\frac{2}{7})^2\right)^6 = (\frac{2}{7})^{12}

.

The left side becomes

(\frac{2}{7})^{-3} \times (\frac{2}{7})^{12} = (\frac{2}{7})^{-3+12} = (\frac{2}{7})^{9}

.

Thus the equation is

(\frac{2}{7})^9 = (\frac{2}{7})^{2m-1}

.

Since bases are equal, equate exponents:

9 = 2m - 1

.

Solve:

2m = 10

, so

m = 5

.

Answer:

m = 5

, which corresponds to option B.

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