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) using only positive integers, you can follow these steps:
Step 1: Simplify the coefficient (numbers) separately.
The coefficient 24 and 42 have a common factor of 6. Divide both by 6 to simplify them:
24 ÷ 6 = 4
42 ÷ 6 = 7
Step 2: Simplify the variables with exponents.
For the variables x, since they have the same base, subtract the exponents:
x^3 ÷ x^7 = x^(3-7) = x^-4
Note that dividing x^3 by x^7 leaves x^-4, since dividing by a larger exponent results in a negative exponent.
For the variables y, since they have the same base, subtract the exponents:
y^2 ÷ y^-6 = y^(2-(-6)) = y^8
When dividing y^2 by y^-6, the negative exponent becomes positive.
Step 3: Combine the simplified coefficient and variables.
Now that we have simplified the coefficient and variables, we can put them all together:
(24x^3y^2) / (42x^7y^-6) = (4x^-4y^8) / (7)
Finally, we have simplified the expression to (4x^-4y^8) / (7), where x^-4 represents 1/x^4 (since the exponent is negative), and 7 is the simplified coefficient.