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What’s the error? A student said that 3⁵/9⁵ is the same as 1/3. What mistake has the student made

Solution:

Given, the expression is 3⁵/9⁵

A student said that 3⁵/9⁵ is the same as 1/3

We have to find the mistake made by the student.

Considering 3⁵/9⁵,

9⁵ can be written as (3 × 3)⁵

For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n,

a^m × b^m = (a × b)^m

(3 × 3)⁵ = 3⁵ × 3⁵

Now, 3⁵/9⁵ = 3⁵/(3⁵ × 3⁵)

Considering 3⁵/3⁵,

For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n,

a^m ÷ aⁿ = a^m-n

= 3^{5 - 5}

= 3⁰

We know a⁰ = 1

So, 3⁰ = 1

Now, 3⁵/(3⁵ × 3⁵) = 1 × (1/3⁵)

= 1/3⁵

1/3 is not same as 1/3⁵

Therefore, the error made by the student is that the base is multiplied by its exponent.

✦ Try This: What’s the error? A student said that 5⁵/25⁵ is the same as 1/5. What mistake has the student made

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 13

NCERT Exemplar Class 7 Maths Chapter 11 Problem 97

What’s the error? A student said that 3⁵/9⁵ is the same as 1/3. What mistake has the student made

Summary:

A student said that 3⁵/9⁵ is the same as 1/3. The mistake made by the student is, 1/3 is not same as 1/3⁵. The error is that the base is multiplied by its exponent.

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