Help please-I'm totally lost-
How would I simplify (2x^5 y^4 z^3/x^-1 y^5 z^5)^-1
Thank you for any help you can give me-I'm so stuck for my homeworkk tonight. I know I can bring up the negatives to top and negative to bottom to make them positive but besides that-I don't get it
Start out with the fraction as written. The wherever there is a negative exponent, swap between numerator and denominator:
(2x5y4z3/x-1y5z5)-1
Invert the fraction:
= x-1y5z5/2x5y4z3
= y5z/2xxyz
= yz/2xyz
Now subtract exponents, leaving the larger portion where it is:
yz/2x
Oops. Lost track of the exponents:
...
y^5 z^5 / 2x^5 x^1 y^4 z^3
y^5 z^5 / 2x^6 y^4 z^3
yz^2/2x^6
Sure, I can help you simplify the expression. Let's break it down step by step.
To simplify the expression (2x^5 y^4 z^3/x^-1 y^5 z^5)^-1, we can start by bringing the negative exponents to the opposite side of the fraction.
The expression becomes (2x^5 y^4 z^3 y^5 z^5/x y^-1)^-1.
Next, let's simplify the terms with the same base. For the variables, we add their exponents when dividing with the same base. So,
(x^5 / x) becomes x^(5-1) which simplifies to x^4.
(y^4 y^5) becomes y^(4+5) which simplifies to y^9.
(z^3 z^5) becomes z^(3+5) which simplifies to z^8.
Now the expression becomes (2x^4 y^9 z^8/x)^-1.
To simplify the expression further, we can use the property of negative exponent, which states that any term raised to the power of -1 is equivalent to its reciprocal. Therefore, the expression becomes:
1/(2x^4 y^9 z^8/x).
Next, we can simplify further by dividing the expression within the parenthesis by x.
The expression becomes 1/(2x^(4-1) y^9 z^8).
Simplifying the exponent, we get 1/(2x^3 y^9 z^8).
So, the simplified expression is 1/(2x^3 y^9 z^8).
I hope this explanation helps you with your homework! Remember, always keep track of the exponent rules and simplify the terms with the same base before applying any other operations.