24x^3y^2/42x^7y^-6 please help i need to simplify i can only use positive intergers
To simplify the expression (24x^3y^2) / (42x^7y^-6), you can follow these steps:
Step 1: Simplify the coefficient (24/42), which can be reduced to its lowest terms. Both numbers are divisible by 6, so divide both by 6:
24 ÷ 6 = 4
42 ÷ 6 = 7
Now, the expression becomes (4x^3y^2) / (7x^7y^-6).
Step 2: Simplify the variables in the numerator and denominator separately.
In the numerator (x^3y^2):
- For the x variable, there are no x variables in the denominator, so we keep it as is.
- For the y variable, there is no y variable in the denominator, so we keep it as is.
In the denominator (7x^7y^-6):
- For the x variable, we need to cancel out as many x variables as possible. Since there are only 3 x variables in the numerator, we need to simplify x^7 to x^3. To do this, we subtract the exponents: 7 - 3 = 4. So, we have x^4 in the denominator.
- For the y variable, we need to cancel out as many y variables as possible. In the numerator, we have y^2, and in the denominator, we have y^-6. To simplify this, let's rewrite y^-6 as 1/y^6. Now, in the denominator, we have y^6. Since we don't have any y variables in the numerator, we bring it to the denominator by changing the exponent sign: y^6 becomes y^-6. Now, we can cancel out y^2 with y^-6, leaving y^(-6 - 2) = y^-8 in the denominator.
After simplifying the variables, the expression becomes:
(4y^2) / (7x^4y^-8)
Step 3: Simplify the expression further by combining the variables.
For variables with the same base (in this case, both y), you can combine them by adding their exponents. Therefore, y^2 / y^-8 can be simplified as follows:
y^2 / y^-8 = y^(2 - (-8)) = y^10
Now, the expression simplifies to:
(4y^2) / (7x^4y^10)
That's the simplified form of the expression (24x^3y^2) / (42x^7y^-6) using positive integers only.