Question

The question says “write with prime number base” and the question is 8 square root 32 (7,d)

Answer 1

`2^{(11)/(2)}`.

Explanation:

We need to write the given expression with prime number base.

In question 7, part d.

The given expression is

`8√(32)`

It can be rewritten as

`2^3√(2^5)`

Using properties of exponents , we get

`2^3(2^5)^{(1)/(2)}`

`2^3(2^{(5)/(2)})`
`[\because \sqrt[n]{x}=x^{\frac{1]{n}}]`

`2^{3+(5)/(2)}`
`[\because (a^m)^n=a^(mn)]`

`2^{(6+5)/(2)}`
`[\because a^ma^n=a^(m+n)]`

`2^{(11)/(2)}`

Here, base is 2 and it is prime number.

Therefore, the required expression is
`2^{(11)/(2)}`.