Simplify the following expression, and rewrite it in an equivalent form with positive exponents.
24x^3y^-3/72x^-5y^-1
My answer was going to be:
24/72*x^3/x^-5=y^=3/y^-1
ashley, I think you need a tutor in person, not online help screens.
do this in parts
real part: 24/72= 1/3
x part: x^3/x^-5= x^8
y part: y^-3/y^-1=1/y^2
answer: 1/3 * x^8/y^2
check that.
I completely agree with you. I am a visual learner and this book is so hard for me to understand it isn't even funny. I am so stressed out and i thank you for your help really.
To simplify the expression and rewrite it in an equivalent form with positive exponents, you can follow these steps:
Step 1: Simplify the coefficients:
The numerator coefficient is 24, and the denominator coefficient is 72. Both 24 and 72 can be divided by their greatest common factor (GCF), which is 24. After division, you get 24/72 = 1/3.
Step 2: Simplify the variables with exponents:
In the numerator, you have x^3 and y^-3, while in the denominator, you have x^-5 and y^-1. To simplify these expressions, you can apply the rule that states x^m/x^n = x^(m-n), and y^m/y^n = y^(m-n).
For x^3/x^-5, subtracting exponents, you get x^(3-(-5)) = x^8.
For y^-3/y^-1, subtracting exponents, you get y^(-3-(-1)) = y^-2.
Step 3: Combine the simplified coefficients and variables:
Now that you have simplified the coefficients and variables, you can combine them to rewrite the expression. The simplified expression is:
(1/3) * (x^8) * (y^-2)
To express the variables with positive exponents, you can move the variables from the denominator to the numerator or vice versa. This involves applying the rule: a^-n = 1/a^n.
Rewriting the expression with positive exponents, you get:
(1/3) * (x^8) * (1/y^2)
This is the simplified expression in an equivalent form with positive exponents.