Answer:
[tex]2^{\frac{11}{2}}[/tex].
Step-by-step explanation:
We need to write the given expression with prime number base.
In question 7, part d.
The given expression is
[tex]8\sqrt{32}[/tex]
It can be rewritten as
[tex]2^3\sqrt{2^5}[/tex]
Using properties of exponents , we get
[tex]2^3(2^5)^{\frac{1}{2}}[/tex]
[tex]2^3(2^{\frac{5}{2}})[/tex] [tex][\because \sqrt[n]{x}=x^{\frac{1]{n}}][/tex]
[tex]2^{3+\frac{5}{2}}[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
[tex]2^{\frac{6+5}{2}}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]2^{\frac{11}{2}}[/tex]
Here, base is 2 and it is prime number.
Therefore, the required expression is [tex]2^{\frac{11}{2}}[/tex].
