Find x so that (5/3)⁵ × (5/3)¹¹ = (5/3)^8x

Solution:

It is given that

(5/3)⁵ × (5/3)¹¹ = (5/3)^8x

We know that

(a/b)^m = a^m/b^m

5⁵/3⁵ × 5¹¹/3¹¹ = (5/3)^8x

(5⁵ × 5¹¹)/ (3⁵ × 3¹¹) = (5/3)^8x

From a^m × aⁿ = a^m+n

5¹⁶/3¹⁶ = (5/3)^8x

(5/3)¹⁶ = (5/3)^8x

Equating both sides

16 = 8x

Dividing both sides by 8

x = 2

Therefore, x = 2.

✦ Try This: Find x so that (7/3)⁴ × (7/3)¹⁰ = (7/3)^12x

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

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NCERT Exemplar Class 7 Maths Chapter 11 Sample Problem 10

Find x so that (5/3)⁵ × (5/3)¹¹ = (5/3)^8x

Summary:

x = 2 so that (5/3)⁵ × (5/3)¹¹ = (5/3)^8x

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