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

Solution:

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

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

RHS: 1/4 (4ⁿ)

1/4 (4ⁿ) can be written as 4ⁿ/4¹.

Using law of exponents,

a^m ÷ aⁿ = a^{m - n}

Here, a = 4

m = n

n = 1

So, m - n = n - 1

Now, 4ⁿ/4¹ = 4^{n - 1}

= LHS

LHS = RHS

Therefore, the given statement is true.

✦ Try This: Use the properties of exponents to verify that each statement is true. 5^{n - 1} = 1/5 (5ⁿ)

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

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

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

Summary:

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

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