Radicals & Rational Exponents Quick Check

Question

2 of 52 of 5 Items
Question
Which of the following is an equivalent expression for 512125√3
when simplified using exponent properties?(1 point)
Responses

50
5 superscript 0 baseline

15
Start Fraction 1 over 5 End Fraction

1
1

5√5

Answer 1

To simplify the expression $512125\sqrt{3}$, we first need to clarify whether the expression is written correctly since it appears to have numbers and a radical.

Assuming you're asking to simplify $512125\cdot \sqrt{3}$ or perhaps to consider bases involving powers, let’s evaluate the term separately:

• $512125$ can be rewritten in terms of its prime factorization, but it's not clear from your question if that’s needed.
• $\sqrt{3}$ can be expressed as $3^{1/2}$.

Now, simplifying $5^2\cdot 5^{1/2}$ gives $5^{2+1/2}=5^{2.5}=5^{5/2}=5^{5/2}$.

However, I will assume we are just focusing on the fractional powers or roots, keeping to what’s presented.

The correct option is not clear from your provided responses, but if we treat the expression as directly simplifying or if attempting roots yields something:

The closest value that could be concluded is:

• If considering only $512$ as $5^0$
• If considering simplifications yield $1$

Given the provided options, the most plausible equivalent expression, when thinking about simplification rules and understanding roots, would likely be:

• 1

However, without more context, it's hard to accurately convey. If you meant something specific with $512125$, please clarify!