So here's the problem:
6a^-2 + 9a^2 all over 3a^-2
The answer is suppose to be 2 + 3a^4
I keep getting the answer as 5.
Can you show me how to solve this problem correctly?
how about multiplying top and bottom of your fraction by a^2 to get
(6 + 9a^4)/3
= 2 + 3a^4
Certainly! Let's break down the problem step by step.
First, let's simplify the expression:
6a^-2 + 9a^2
To do this, we need to use the rules of exponents. The rule for negative exponents states that any number raised to a negative exponent can be rewritten as the reciprocal of the number raised to the positive exponent. So, in this case, we can rewrite a^-2 as 1/a^2.
Now the expression becomes:
6(1/a^2) + 9a^2
Next, let's simplify the expression further by finding a common denominator for the fractions. The common denominator in this case is a^2. To do this, we need to multiply the first fraction by a^2/a^2:
(6(1/a^2) * a^2/a^2) + 9a^2
This simplifies to:
6a^2/a^2 + 9a^2
Now we can combine the fractions:
6a^2/a^2 + 9a^2 = (6a^2 + 9a^2) / a^2
This simplifies to:
(6a^2 + 9a^2) / a^2 = 15a^2 / a^2
Finally, we can cancel out the common factor of a^2 in the numerator and denominator, resulting in:
15a^2 / a^2 = 15
So the correct answer is 15, not 5.
It seems there was an error in the given answer. To verify this, let's calculate the correct answer using the original expression:
(6a^-2 + 9a^2) / 3a^-2
Using the same steps as before:
(6a^-2 + 9a^2) / 3a^-2 = (6(1/a^2) + 9a^2) / 3(1/a^2)
Simplifying further:
(6(1/a^2) + 9a^2) / 3(1/a^2) = (6a^2 + 9a^2) / (3/a^2)
Multiplying by the reciprocal of 3/a^2:
(6a^2 + 9a^2) / (3/a^2) = (15a^2) * (a^2/3)
This simplifies to:
(15a^2) * (a^2/3) = (15/3) * (a^2 * a^2)
And simplifying further:
(15/3) * (a^2 * a^2) = 5 * (a^4)
So the correct answer is indeed 5a^4, not 2 + 3a^4.
I apologize for any confusion caused by the given answer.