Question

Find the value of p if [2/5]³×[2/5]^-6=[2/5]²p-¹​

Answer 1

Answer:

Step-by-step explanation:

Given -

(2/5)^3 × (2/5)^-6 = (2/5)^2p - 1

To Find -

Value of p

As we know that :-

a^p × a^q = a^p+q

It means,

» (2/5)^3 × (2/5)^-6 = (2/5)^2p-1

» (2/5)^3-6 = (2/5)^2p-1

» (2/5)^-3 = (2/5)^2p-1

As we see that here base is equal

So,

» - 3 = 2p - 1

» - 3 + 1 = 2p

» - 2 = 2p

» p = -2/2

» p = -1

Hence,

The value of p is -1

Verification -

(2/5)^3 × (2/5)^-6 = (2/5)^2p-1

» (2/5)^3-6 = (2/5)^2×-1 -1

» (2/5)^-3 = (2/5)^-2-1

» (2/5)^-3 = (2/5)^-3

Hence,

Verified..

Formula Used :-

a^p × a^q = a^p+q

Some related formulas :-

a^p ÷ a^q = a^p-q

(a^p)^q = a^pq

a^pb^p = (ab)^p