Use the Quotient Property to generate an equivalent expression to 9 3/5|9 1/5
What is the simplified exponent?
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.
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.
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)
To generate an equivalent expression using the Quotient Property, we divide the two fractions (9 3/5) and (9 1/5).
First, convert the mixed numbers to improper fractions:
9 3/5 = (9 * 5 + 3)/5 = 48/5
9 1/5 = (9 * 5 + 1)/5 = 46/5
Now divide the two fractions:
(48/5) / (46/5) = (48/5) * (5/46) = 48/46
The simplified exponent in this case would be 48/46.
To use the Quotient Property to generate an equivalent expression, we divide the two given numbers and subtract their exponents.
First, let's convert the mixed numbers to improper fractions:
9 3/5 = (9*5 + 3)/5 = 48/5
9 1/5 = (9*5 + 1)/5 = 46/5
Now, to find the equivalent expression using the Quotient Property, we divide 48/5 by 46/5:
(48/5) / (46/5)
To divide fractions, we invert the divisor (the second fraction) and multiply:
(48/5) * (5/46)
Simplifying the expression, we cancel out the common factor of 5 in the numerator and denominator:
(48 * 1) / (1 * 46) = 48/46
To simplify this fraction further, we can find the highest common factor (HCF) of 48 and 46, which is 2.
Dividing both the numerator and denominator by 2, we get:
(48/2) / (46/2) = 24/23
So, the equivalent expression to 9 3/5 divided by 9 1/5 is 24/23.
Now, moving on to finding the simplified exponent. Unfortunately, there is no mention of any exponents in the given problem. If you could provide more information or clarify the question, I would be happy to help you further.