What expressions are equivalent to 16 5/2

Question

A 4^5

B 8^5

C square root of 16^5

D 5 square root of 16^2

E (16^2) (16 1/2)

F (16^5) (16 1/2)

Answer 1

Good morning. I believe you are asking which expressions are equivalent to 16^5/2. If this is the case, the expression is currently in rational exponent form. It can be rewritten in radical form as (√16)⁵ (that is the square root of 16 to the 5th power, Choice C). Since √16 = 4, that expression can now be written as 4⁵(Choice A), which is equal to 1,024.

Also, using the product property for exponents: a^m · aⁿ = a^m+n, we can rewrite 16^5/2 as 16^{4/2 + 1/2} or 16^{2 + 1/2}, then we can rewrite that using the rule as 16² · 16^1/2(Choice E).

So A, C, and E are equivalent.

To verify that those are the only choices that are equivalent to 16^5/2, you can also evaluate all of the other expressions in the choices:

B. 8⁵ = 32,768

D. The 5th root of 16² is approximately 3.031

F. 16⁵ · 16^1/2 = 1,048,576 · 4 = 4,194,304

I hope this helps. Please let me know if you need any further clarification.