Question

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

Answer 1

Answer:

$2^{\frac{11}{2}}$.

Step-by-step explanation:

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

In question 7, part d.

The given expression is

$8\sqrt{32}$

It can be rewritten as

$2^3\sqrt{2^5}$

Using properties of exponents , we get

$2^3(2^5)^{\frac{1}{2}}$

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

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

$2^{\frac{6+5}{2}}$    $[\because a^ma^n=a^{m+n}]$

$2^{\frac{11}{2}}$

Here, base is 2 and it is prime number.

Therefore, the required expression is $2^{\frac{11}{2}}$.