Question

Simplify sqrt (8^17)

a) 8^8 sqrt(8)
b) 8^7 sqrt(8)
c) 2^3 sqrt (8)
d) 2^5 sqrt (8^2)​

Answer 1

a on edge 2021

Explanation:

took the test

Answer 2

a)
`8^8√(8)`

Explanation:

Given,

`\sqrt{8^1^7`

We have to simplify the expression by using "The Law of Indices".

`x^m* x^n=x^m^+^n`

So we can rewrite the expression as,

`\sqrt{8^1^7`=
`√(8^1^+^1^6) =√(8)* √(8^1^6)`

Now according to law of indices, which is;

`(x^m)^n=x^m^n`

So we can rewrite the expression as

`√(8)* √(8^1^6)=√(8)* (8^1^6)^(1)/(2) \ \ \ \ Or\ \ \ √(8)* 8^{16*(1)/(2)} = 8^8\sqrt{8`

Hence the final Answer is
`8^8\sqrt{8`.