Divide and check. Write your answer using non negative exponents 40x^2y^2/5x^4y^2. Thank you.
To divide the expression (40x^2y^2) / (5x^4y^2) and write the answer using non-negative exponents, you need to apply the rule of exponents for division:
The rule states that when dividing two terms with the same base, you subtract the exponents.
Let's break down the expression step by step:
Step 1: Divide the numerical coefficients:
40 / 5 = 8
Step 2: Divide the x terms:
x^2 / x^4 = x^(2-4) = x^(-2)
Step 3: Divide the y terms:
y^2 / y^2 = y^(2-2) = y^0
Remember that any number or variable raised to the power of 0 is equal to 1.
Now, we combine all the results:
8x^(-2)y^0
Since any term raised to the power of 0 is equal to 1, we can simplify further:
8x^(-2)y^0 = 8x^(-2) * 1 = 8x^(-2) = 8 / x^2
Therefore, the division of (40x^2y^2) / (5x^4y^2) can be expressed as 8 / x^2, where the exponent of x is 2 and it is written with a non-negative exponent.