Use the properties of exponents to verify that each statement is true.
1/4 (2ⁿ) = 2^{n - 2}

Solution:

Given, the statement is 1/4 (2ⁿ) = 2^{n - 2}

We have to determine if the given statement is true using the properties of exponents.

LHS: 1/4 (2ⁿ)

We know, 4 = 2²

So, 1/4 (2ⁿ) = 2ⁿ/2²

Using law of exponents,

a^m ÷ aⁿ = a^{m - n}

Here, a = 2

m = n

n = 2

So, m - n = n - 2

Now, 2ⁿ/2² = 2^{n - 2}

= RHS

LHS = RHS

Therefore, the given statement is true.

✦ Try This: Use the properties of exponents to verify that each statement is true. 1/9 (3ⁿ) = 3^{n - 2}

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

NCERT Exemplar Class 8 Maths Chapter 8 Problem 143(a)

Use the properties of exponents to verify that each statement is true. 1/4 (2ⁿ) = 2^{n - 2}

Summary:

The given statement, ”1/4 (2ⁿ) = 2^{n - 2}” is true using the law of exponents a^m ÷ aⁿ = a^{m - n}

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