Question

Please can anyone send a question in law of indices I really need it now​

Answer 1

I think this is a pretty good question of law of indices

Explanation:

Given that

`(9^p)(27^q)=3^n\\`

a) express n in terms of p and q ,

b) hence if p = 1 and q = 2 find the value of n

Solution to part a)

`(9^p)(27^q)=3^n\\\\`

Simplify the equation and how do we do that? As we can see that 9 can also be written as 3^2 and 27 can be written as 3^3 we can rewrite the following equation like this,

`(3^2)^p(3^3)^q=3^n\\`

now we multiply p with 2 and

multiply q with 3 respectively,

`(3^(2p))(3^(3q))=3^n\\`

now since the bases are same and are multiplying the exponents will add themselves like this, in this equation the number 3 is the base

`3^(2p+3q)=3^n\\`

now since the bases on the left hand side and on the right hand side are equal the exponents will also be equal so now,

`2p+3q=n\\`

hence n is expressed in terms of p and q

Solution to part b)

if p = 1 and q = 2 we plug in these values in the above equation we found for n

n = 2p + 3q

n = 2(1) + 3(2)

n = 2 + 6

n = 7