Simplify the following exponents and rewrite it in an equivalent form with positive exponents..24x^3y^-3/72x^-5y^-1
I will assume you meant
(24x^3y^-3)/(72x^-5y^-1) , the way you have it, it would be divided by only 72
= (1/3)x^8 / y^2
or
= x^8 / (3y^2)
Yes Reiny that is correct
To simplify the expression and rewrite it with positive exponents, we can start by canceling out common factors in the numerator and denominator:
24x^3y^-3 / 72x^-5y^-1
We can simplify each factor separately:
24/72 simplifies to 1/3.
x^3 / x^-5 can be simplified by subtracting the exponents, which gives us x^(3 - (-5)) = x^8.
y^-3 / y^-1 can be simplified by subtracting the exponents, which gives us y^(-3 - (-1)) = y^-2 = 1/y^2.
Now, we can rewrite the expression with positive exponents:
(1/3) * x^8 * (1/y^2)
This can be written as:
x^8 / (3y^2)
To simplify the given expression and rewrite it in an equivalent form with positive exponents, we need to follow certain rules of exponents.
Let's break down the expression step by step:
Expression: 24x^3y^-3/72x^-5y^-1
Step 1: Simplify the numerator.
In the numerator, we have x^3 and y^-3. To simplify y^-3, we can move it to the denominator by changing its sign to positive: 1/y^3.
Now we have: 24x^3/72x^-5y^-1 * 1/y^3
Step 2: Simplify the denominator.
In the denominator, we have x^-5 and y^-1. We can move both of these terms to the numerator by changing their signs to positive: x^5y^1.
Now we have: 24x^3 * x^5y^1 / 72 * y^3
Step 3: Simplify the expression.
To simplify the expression, we combine the like terms. In this case, we can multiply the coefficients and add the exponents with the same base.
The coefficient in the numerator is 24, and the coefficient in the denominator is 72. Their simplified form is 1/3 (24 divided by 72).
The x-terms have a base of x, so we add the exponents: x^3 * x^5 = x^(3+5) = x^8.
The y-terms have a base of y, so we add the exponents: y^1 * y^3 = y^(1+3) = y^4.
The simplified expression is: (1/3)x^8y^4.
So, the original expression, 24x^3y^-3/72x^-5y^-1, simplifies to:
(1/3)x^8y^4.