Question
Radicals & Rational Exponents Quick Check 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 1 1 15 Start Fraction 1 over 5 End Fraction 5√5 Start Fraction Start Root 5 End Root over 5 End Fraction 50
Answers
GPT-4o mini
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.
1. **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,
\[ 512125 = 2^9 \times 5^3 \]
2. **Dealing with \( \sqrt{3} \):**
- The square root of \( 3 \) can be written in exponential form as \( 3^{1/2} \).
3. **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!
However, if you're looking to express everything in exponential form, we can break down the components.
1. **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,
\[ 512125 = 2^9 \times 5^3 \]
2. **Dealing with \( \sqrt{3} \):**
- The square root of \( 3 \) can be written in exponential form as \( 3^{1/2} \).
3. **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!