Hello, I have two more rational exponent question that I wanted to verify please:
4x^3y^-2
_________
2x^-1y^4
= 2x^4y^6
is this correct?
2nd question:
[w^1 / w^-3]
my answer:
= [w^(1)(-4)/ w ^ (-3)(-4)]
= w^-4 / w^12
= w^12 / w^4
= w^3 / w
Is this right?
Both are wrong. You seem to have no idea at all how to handle exponents.
The answers are
2x^4 y^-6 and w^4.
Well aren't you special to tell me that. You seem to have no idea how to treat people. Hmmm, which deficite would I rather have. Thanks for the disrespectful help. I don't think you should tutor anyone.
To verify the first question, let's simplify the expression step by step:
The given expression is (4x^3y^-2) / (2x^-1y^4).
Step 1: Divide the numbers in the numerator and denominator: 4 / 2 = 2.
Step 2: Apply the exponent rules for variables.
In the numerator, we have x^3 divided by x^-1. Using the rule x^m / x^n = x^(m-n), we subtract the exponents: x^3 / x^-1 = x^(3-(-1)) = x^4.
In the denominator, we have y^-2 divided by y^4. Applying the rule y^m / y^n = y^(m-n), we subtract the exponents: y^-2 / y^4 = y^(-2-4) = y^-6 = 1/y^6.
Step 3: Simplify the final expression.
We have 2x^4y^-6. Remember that y^-6 is the same as 1/y^6, so we can rewrite it as 2x^4 / (y^6).
Therefore, the simplified expression is 2x^4 / y^6.
To verify your answer, we can compare it with the simplified expression. In this case, your answer 2x^4y^6 is not correct.
Moving on to the second question, we have [w^1 / w^-3].
Step 1: Apply the exponent rule for division. When dividing variables with the same base, we subtract the exponents: w^1 / w^-3 = w^(1-(-3)) = w^4.
Therefore, the simplified expression is w^4.
Now, let's verify your solution step by step:
Your answer begins correctly, applying the exponent rule for division: w^(1)(-4) / w^(-3)(-4). However, there seems to be a mistake in the next step.
The correct simplification should be:
w^(-4) / w^12
Since w^(-4) is equal to 1 / w^4, we can rewrite the expression as:
(1 / w^4) / w^12 = 1 / (w^4 * w^12) = 1 / w^16
So, the correct answer is 1 / w^16, not w^12 / w^4 or w^3 / w.
In summary, the correct answer for the second question is w^4, and your answer is incorrect.