Question
Simplify
х8
xet
(1 point)
Because there are 8 factors of x in the numerator and 4 factors of x in the denominator, when the X's cancel you are left with x 1
Because when you are dividing with exponents, you should add the exponents so that you are left with x'2
Because the numerator has an exponent of 8 and the denominator has an exponent of 4, when you divide you are left with x?
Because there are 8 factors of x in the numerator and 4 factors of x in the denominator, when the X's cancel you are left with at
х8
xet
(1 point)
Because there are 8 factors of x in the numerator and 4 factors of x in the denominator, when the X's cancel you are left with x 1
Because when you are dividing with exponents, you should add the exponents so that you are left with x'2
Because the numerator has an exponent of 8 and the denominator has an exponent of 4, when you divide you are left with x?
Because there are 8 factors of x in the numerator and 4 factors of x in the denominator, when the X's cancel you are left with at
Answers
GPT-4o mini
To simplify the expression \( \frac{x^8}{x^4} \), you can use the properties of exponents. Specifically, when you divide with the same base, you subtract the exponents:
\[
\frac{x^8}{x^4} = x^{8-4} = x^4
\]
So the simplified form is \( x^4 \).
Considering your response options:
1. **Because there are 8 factors of x in the numerator and 4 factors of x in the denominator, when the X's cancel you are left with x^4** (Correct rationale based on cancellation of like factors).
2. **Because when you are dividing with exponents, you should add the exponents so that you are left with x^2** (Incorrect operation; should be subtraction).
3. **Because the numerator has an exponent of 8 and the denominator has an exponent of 4, when you divide you are left with x^4** (Correct reasoning).
4. **Because there are 8 factors of x in the numerator and 4 factors of x in the denominator, when the X's cancel you are left with x^4** (Same as option 1, correct).
Thus the best options are the first and fourth since they correctly describe the reasoning leading to \( x^4 \) as the simplified answer.
\[
\frac{x^8}{x^4} = x^{8-4} = x^4
\]
So the simplified form is \( x^4 \).
Considering your response options:
1. **Because there are 8 factors of x in the numerator and 4 factors of x in the denominator, when the X's cancel you are left with x^4** (Correct rationale based on cancellation of like factors).
2. **Because when you are dividing with exponents, you should add the exponents so that you are left with x^2** (Incorrect operation; should be subtraction).
3. **Because the numerator has an exponent of 8 and the denominator has an exponent of 4, when you divide you are left with x^4** (Correct reasoning).
4. **Because there are 8 factors of x in the numerator and 4 factors of x in the denominator, when the X's cancel you are left with x^4** (Same as option 1, correct).
Thus the best options are the first and fourth since they correctly describe the reasoning leading to \( x^4 \) as the simplified answer.