Question
Simplify u75/y30
.(1 point)
Responses
uy45
u y superscript 45 baseline
u75/y30
Start Fraction u superscript 75 baseline over y superscript 30 baseline End Fraction
u45
u superscript 45 baseline
45
.(1 point)
Responses
uy45
u y superscript 45 baseline
u75/y30
Start Fraction u superscript 75 baseline over y superscript 30 baseline End Fraction
u45
u superscript 45 baseline
45
Answers
GPT-4o mini
To simplify the expression \(\frac{u^{75}}{y^{30}}\), we treat each part separately:
1. The numerator is \(u^{75}\).
2. The denominator is \(y^{30}\).
This expression cannot be simplified further as it does not involve common bases in the numerator and denominator.
If you want to express it differently using exponents, consider the following:
1. The bases are different: \(u\) and \(y\).
2. The expression already appears simplified.
Thus, the simplified expression remains \(\frac{u^{75}}{y^{30}}\).
If we wanted to express \(u^{75}\) in terms of \(u^{45}\), we can say:
\[
u^{75} = u^{45} \cdot u^{30}
\]
However, your question seems to emphasize "simplifying" rather than transforming the expression into a product, which means the answer is best left in its form. So, among the given options, \(\frac{u^{75}}{y^{30}}\) is the simplest form.
If you wanted to keep it in a base of \(u\):
- The closest representation from your list would be \(u^{45}\), but this does not accurately represent the original expression.
Therefore, the most correct answer reflecting the expression you presented is:
**\( \frac{u^{75}}{y^{30}} \)** or simply keep it as is.
1. The numerator is \(u^{75}\).
2. The denominator is \(y^{30}\).
This expression cannot be simplified further as it does not involve common bases in the numerator and denominator.
If you want to express it differently using exponents, consider the following:
1. The bases are different: \(u\) and \(y\).
2. The expression already appears simplified.
Thus, the simplified expression remains \(\frac{u^{75}}{y^{30}}\).
If we wanted to express \(u^{75}\) in terms of \(u^{45}\), we can say:
\[
u^{75} = u^{45} \cdot u^{30}
\]
However, your question seems to emphasize "simplifying" rather than transforming the expression into a product, which means the answer is best left in its form. So, among the given options, \(\frac{u^{75}}{y^{30}}\) is the simplest form.
If you wanted to keep it in a base of \(u\):
- The closest representation from your list would be \(u^{45}\), but this does not accurately represent the original expression.
Therefore, the most correct answer reflecting the expression you presented is:
**\( \frac{u^{75}}{y^{30}} \)** or simply keep it as is.