To simplify the expression \( 512125\sqrt{3} \) using exponent properties, let's first clarify if there's a need to simplify \( 512125 \) and \( \sqrt{3} \) in the same step.
However, if you're looking to express everything in exponential form, we can break down the components.
- Expressing \( 512125 \):
- By inspecting \( 512125 \), it looks like a composite number or product of terms, and we should find its prime factorization or suitable representation.
- To verify, \( 512 = 2^9 \) and \( 125 = 5^3 \), therefore: \[ 512125 = 512 \times 125 = 2^9 \times 5^3 \]
Thus, \[ 512125 = 2^9 \times 5^3 \]
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Dealing with \( \sqrt{3} \):
- The square root of \( 3 \) can be written in exponential form as \( 3^{1/2} \).
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Combining the two parts:
- The entire expression simplifies to: \[ 512125\sqrt{3} = 2^9 \times 5^3 \times 3^{1/2} \]
Since you only provided several outcomes without the full options needed, let's focus on the forms given:
If you can provide the options in the responses more clearly or in full, I can help identify which one matches this simplification. Based on what we have:
Ultimately, if you meant these values as they relate to fractional forms lodged under roots or radicals, no such direct linear simplification appears in this case without context.
If in-radical form or a coupling with \( \sqrt{5} \) or similar occurs, let’s clarify those responses further or consider your options to summarize that below.
Finalize the options or check those forms and let’s resolve them fittingly!
1 answer