Find the value of x so that (5/3)^-2 × (5/3)^-14 = (5/3)^8x.

Solution:

Given, the expression is (5/3)^-2 × (5/3)^-14 = (5/3)^8x.

We have to find the value of x.

LHS: (5/3)^-2 × (5/3)^-14

Using law of exponents,

a^m × aⁿ = a^{m + n}

From the expression (5/3)^-2 × (5/3)^-14,

a = 5/3

m = -2

n = -14

So, m + n = -2 + (-14)

= -16

a^{m + n} = (5/3)^-16

RHS: (5/3)^8x

(5/3)^-16 = (5/3)^8x

Now, 8x = -16

x = -16/8

x = -2

Therefore, the value of x is -2.

✦ Try This: Find the value of x so that (5)^-3 × (5)^-15 = (5/3)^4x

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

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NCERT Exemplar Class 8 Maths Chapter 8 Problem 99(i)

Find the value of x so that (5/3)^-2 × (5/3)^-14 = (5/3)^8x

Summary:

The value of x so that (5/3)^-2 × (5/3)^-14 = (5/3)^8x is -2 using the law of exponents

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