24x^3y^2/42x^7y^-6 please help i need to simplify i can only use positive intergers
To simplify the expression, you can simplify the coefficients (24 and 42) and simplify the variables separately (x^3 and x^7, y^2 and y^-6), and then combine them.
Let's start with the coefficients:
24 divided by 6 equals 4, and 42 divided by 6 equals 7. So the simplified coefficient is 4/7.
Now let's look at the variables:
For x, we have x^3 divided by x^7. When we divide variables with the same base, we subtract the exponents. So x^3 divided by x^7 can be written as x^(3-7), which simplifies to x^-4. Remember that negative exponents indicate the reciprocal, so x^-4 is equal to 1/x^4.
For y, we have y^2 divided by y^-6. Similar to x, we subtract the exponents when dividing variables with the same base. So y^2 divided by y^-6 can be written as y^(2-(-6)), which simplifies to y^8.
Now we can put it all together:
The simplified expression is (4/7) * (1/x^4) * y^8.
It's important to note that if the original expression didn't have any restrictions on the variables (e.g., positive integers only), we would keep the variables in the simplified expression as they are. But since we can only use positive integers, we need to convert the negative exponents to positive exponents.
So the final simplified expression, using only positive exponents, is:
(4/7) * (y^8 / x^4).