Question
Use the quotient property to generate an equivalent expression to 9 3/5/9 1/5 what is the simplified exponent in fraction form
Answers
Answer
Sorry the exponents are the two fractions 3/5 and 1/5
Answered by
GPT-4o mini
To simplify the expression \( \frac{9 \frac{3}{5}}{9 \frac{1}{5}} \) using the quotient property, we start by converting the mixed numbers into improper fractions.
1. Convert \( 9 \frac{3}{5} \) to an improper fraction:
\[
9 \frac{3}{5} = 9 + \frac{3}{5} = \frac{9 \times 5 + 3}{5} = \frac{45 + 3}{5} = \frac{48}{5}
\]
2. Convert \( 9 \frac{1}{5} \) to an improper fraction:
\[
9 \frac{1}{5} = 9 + \frac{1}{5} = \frac{9 \times 5 + 1}{5} = \frac{45 + 1}{5} = \frac{46}{5}
\]
3. Now substitute these improper fractions back into the original expression:
\[
\frac{9 \frac{3}{5}}{9 \frac{1}{5}} = \frac{\frac{48}{5}}{\frac{46}{5}}
\]
4. Since we are dividing by a fraction, we can multiply by its reciprocal:
\[
\frac{48}{5} \times \frac{5}{46} = \frac{48 \times 5}{5 \times 46}
\]
5. The \( 5 \) in the numerator and denominator cancels out:
\[
= \frac{48}{46}
\]
6. We can simplify \( \frac{48}{46} \):
\[
\frac{48}{46} = \frac{24}{23}
\]
So, the equivalent expression for \( \frac{9 \frac{3}{5}}{9 \frac{1}{5}} \) is \( \frac{24}{23} \).
If you meant to find the exponent form of this simplification, note that this particular expression does not relate to exponents. If exponents weren't intended and if you meant something different, please clarify. However, based on the context, the simplified fraction form is:
\[
\frac{24}{23}
\]
1. Convert \( 9 \frac{3}{5} \) to an improper fraction:
\[
9 \frac{3}{5} = 9 + \frac{3}{5} = \frac{9 \times 5 + 3}{5} = \frac{45 + 3}{5} = \frac{48}{5}
\]
2. Convert \( 9 \frac{1}{5} \) to an improper fraction:
\[
9 \frac{1}{5} = 9 + \frac{1}{5} = \frac{9 \times 5 + 1}{5} = \frac{45 + 1}{5} = \frac{46}{5}
\]
3. Now substitute these improper fractions back into the original expression:
\[
\frac{9 \frac{3}{5}}{9 \frac{1}{5}} = \frac{\frac{48}{5}}{\frac{46}{5}}
\]
4. Since we are dividing by a fraction, we can multiply by its reciprocal:
\[
\frac{48}{5} \times \frac{5}{46} = \frac{48 \times 5}{5 \times 46}
\]
5. The \( 5 \) in the numerator and denominator cancels out:
\[
= \frac{48}{46}
\]
6. We can simplify \( \frac{48}{46} \):
\[
\frac{48}{46} = \frac{24}{23}
\]
So, the equivalent expression for \( \frac{9 \frac{3}{5}}{9 \frac{1}{5}} \) is \( \frac{24}{23} \).
If you meant to find the exponent form of this simplification, note that this particular expression does not relate to exponents. If exponents weren't intended and if you meant something different, please clarify. However, based on the context, the simplified fraction form is:
\[
\frac{24}{23}
\]
Answered by
GPT-4o mini
No problem! Let's use the exponents \( \frac{3}{5} \) and \( \frac{1}{5} \) that you mentioned to generate an equivalent expression and simplify it using the quotient property of exponents.
The expression you'd like to consider is:
\[
\frac{9^{\frac{3}{5}}}{9^{\frac{1}{5}}}
\]
According to the quotient property of exponents, when you divide powers with the same base, you subtract the exponents:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
### Applying the Quotient Property
Using the above property for our expression:
\[
\frac{9^{\frac{3}{5}}}{9^{\frac{1}{5}}} = 9^{\frac{3}{5} - \frac{1}{5}}
\]
Now, let's simplify the exponent:
\[
\frac{3}{5} - \frac{1}{5} = \frac{3 - 1}{5} = \frac{2}{5}
\]
### Final Expression
Thus, we can express it as:
\[
9^{\frac{2}{5}}
\]
So the simplified exponent in fraction form is \( \frac{2}{5} \).
The expression you'd like to consider is:
\[
\frac{9^{\frac{3}{5}}}{9^{\frac{1}{5}}}
\]
According to the quotient property of exponents, when you divide powers with the same base, you subtract the exponents:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
### Applying the Quotient Property
Using the above property for our expression:
\[
\frac{9^{\frac{3}{5}}}{9^{\frac{1}{5}}} = 9^{\frac{3}{5} - \frac{1}{5}}
\]
Now, let's simplify the exponent:
\[
\frac{3}{5} - \frac{1}{5} = \frac{3 - 1}{5} = \frac{2}{5}
\]
### Final Expression
Thus, we can express it as:
\[
9^{\frac{2}{5}}
\]
So the simplified exponent in fraction form is \( \frac{2}{5} \).
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