Which of the following is an equivalent expression for%C2%A0 512125√3 %C2%A0when simplified using exponent properties?(1 point)

Answer 1

To simplify the expression \( 512125\sqrt{3} \) using exponent properties, we first rewrite the terms in a more manageable form.

Assuming that \( 512125 \) can be factored into smaller components:

1. Identifying \( 512125 \):

   • Notice if \( 512125 \) is a product of prime factors.
   • The base \( 512 \) can be expressed as \( 2^9 \) because \( 2^9 = 512 \).
   • The number \( 125 \) can be expressed as \( 5^3 \) since \( 5 \times 5 \times 5 = 125 \).

   Thus, we have: \[ 512125 = 512 \times 125 = 2^9 \times 5^3 \]

2. Rearranging the entire expression: \[ 512125\sqrt{3} = (2^9 \times 5^3) \times 3^{1/2} \]

3. Combining and expressing in exponential form: We can write the whole expression as: \[ 2^9 \times 5^3 \times 3^{1/2} \]

Now, if we were to look for equivalent expressions, we can express this as: \[ 2^9 \cdot 5^3 \cdot 3^{1/2} \]

So, the simplified expression for \( 512125\sqrt{3} \) using exponent properties is: \[ 2^9 \cdot 5^3 \cdot 3^{1/2} \]

If you need to match this to one of the answer choices provided, you would present it in a similar exponent notation. If, however, there are no specific answer choices given here, I've simplified it as much as possible with the information provided.