Question
Use the Quotient Property to generate an equivalent expression to 9 3/5|9 1/5
What is the simplified exponent?
What is the simplified exponent?
Answers
Answered by
GPT 3.5
The Quotient Property states that for any two numbers a and b, if a/b is the original fraction or mixed number, then the equivalent expression using the Quotient Property is ab.
Using this property, the equivalent expression to 9 3/5 ÷ 9 1/5 is (9 + 3/5) × (5/9 + 1/5).
To simplify this expression, we can combine the fractions inside the parentheses:
(9 + 3/5) × (5/9 + 1/5) = (45/5 + 3/5) × (5/9 + 1/5) = (48/5) × (5/9 + 1/5)
Now, to multiply these fractions, we can multiply the numerators together and multiply the denominators together:
(48/5) × (5/9 + 1/5) = (48 × 5) / (5 × 9 + 5 × 1) = 240/45
Simplifying this fraction further, we can divide both the numerator and the denominator by their greatest common divisor, which is 5:
240/45 = (240 ÷ 5) / (45 ÷ 5) = 48/9
Therefore, the simplified expression is 48/9.
The simplified exponent for this expression is 48/9.
Using this property, the equivalent expression to 9 3/5 ÷ 9 1/5 is (9 + 3/5) × (5/9 + 1/5).
To simplify this expression, we can combine the fractions inside the parentheses:
(9 + 3/5) × (5/9 + 1/5) = (45/5 + 3/5) × (5/9 + 1/5) = (48/5) × (5/9 + 1/5)
Now, to multiply these fractions, we can multiply the numerators together and multiply the denominators together:
(48/5) × (5/9 + 1/5) = (48 × 5) / (5 × 9 + 5 × 1) = 240/45
Simplifying this fraction further, we can divide both the numerator and the denominator by their greatest common divisor, which is 5:
240/45 = (240 ÷ 5) / (45 ÷ 5) = 48/9
Therefore, the simplified expression is 48/9.
The simplified exponent for this expression is 48/9.
Answered by
oobleck
These humans need to learn to type math. Your solution is nice, but the question mentioned exponents. I'm pretty sure that the expression was supposed to be
9^(3/5) / 9^(1/5) = 9^(3/5 - 1/5) = 9^(2/5)
9^(3/5) / 9^(1/5) = 9^(3/5 - 1/5) = 9^(2/5)
Answered by
GPT 3.5
You are correct, my apologies for the oversight. Thank you for pointing out the mistake.
To generate an equivalent expression using the Quotient Property for 9^(3/5) / 9^(1/5), we can subtract the exponents since they have the same base, 9:
9^(3/5) / 9^(1/5) = 9^(3/5 - 1/5) = 9^(2/5)
Therefore, the simplified exponent is 2/5.
To generate an equivalent expression using the Quotient Property for 9^(3/5) / 9^(1/5), we can subtract the exponents since they have the same base, 9:
9^(3/5) / 9^(1/5) = 9^(3/5 - 1/5) = 9^(2/5)
Therefore, the simplified exponent is 2/5.