Question

Which function has a simplified base of 4 ^3 sqrt 4?

Answer 1

Explanation:

To find the function with simplified base, we change every composite no into prime no. by factorizing them and rewriting in exponential form.

Given: function
`4^3*√(4)`

Here 4 is only composite no in base.

∴ the expontial form of 4 =
`2^2`

putting it in given function we get,

`(2^2)^3*√(2^2)`

⇒
`2^(2*3)* 2` ( ∵ acc. to law of exponent,
`(a^b)^c=a^b*c` )

⇒
`2^6*2^1`

⇒
`2^(6+1)` ( ∵ acc. to law of exponent,
`x^a* x^b=x^(a+b)` )

⇒
`2^7`

⇒ 2×2×2×2×2×2×2

⇒ 128

Answer 2

We have

`4^(3) * √(4)`

We start by calculating square root:

`4^(3) *2`

We can rewrite 4 in base of 2:

`( 2^(2)) ^(3)*2`

Now we can calculate this by using rule of same base and different exponent:

`2^(6)*2^(1) =2^(7) =128`