Simplify -(2xy^3)^-5
A: -32x^5y^15
B: -32/x^5y^15
C: -1/32x^5y^15
D: -1/32x^4y^2
I have a good understanding of Exponents, its just that I don't get this one. I feel like it is C but at the same time I feel like it is B. I got C though but I don't understand how they got -1 on top. I know that D and A are out. Please help!
-1/(2xy^3)^5
-1/(32x^5y^15)
C is correct.
To simplify -(2xy^3)^-5, let's break it down step by step:
Step 1: Evaluate the expression inside the parentheses:
(2xy^3)^-5 = 1/(2xy^3)^5
Step 2: Apply the exponent to each term inside the parentheses:
= 1/(2^5 * (x^1)^5 * (y^3)^5)
= 1/(32 * x^5 * y^15)
Step 3: Apply the negative sign outside the parentheses:
= -1/(32 * x^5 * y^15)
So the simplified form of -(2xy^3)^-5 is C: -1/32x^5y^15.
Now let's address your confusion about the numerator and denominator:
In the given expression, we have -(2xy^3)^-5. When we put the expression in fraction form (as required to simplify), the negative sign applies to the entire fraction. That is why we have -1 as the numerator.
For the denominator, we have 32 * x^5 * y^15 because all the terms inside the parentheses get multiplied. You are correct to eliminate option B because it has the wrong placement of the negative sign.
So, to summarize, the answer is indeed C: -1/32x^5y^15.