Use the properties of exponents to verify that each statement is true.
25(5^{n - 2}) = 5ⁿ

Solution:

Given, the statement is 25(5^{n - 2}) = 5ⁿ

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

LHS: 25(5^{n - 2})

We know, 25 = 5²

25(5^{n - 2}) = 5² × 5^{n - 2}

Using law of exponents,

a^m × aⁿ = a^{m + n}

Here, a = 5

m = 2

n = n - 2

So, m + n = 2 + (n - 2)

= 2 - 2 + n

= n

So, 5² × 5^{n - 2} = 5ⁿ

= RHS

LHS = RHS

Therefore, the given statement is true.

✦ Try This: Use the properties of exponents to verify that each statement is true. 16(4^{n - 2}) = 4ⁿ

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

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

Use the properties of exponents to verify that each statement is true. 25(5^{n - 2}) = 5ⁿ

Summary:

The given statement, ”25(5^{n - 2}) = 5ⁿ” is true using the law of exponents a^m × aⁿ = a^m+n

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