Divide and check. Write your answer using none negative exponents.
40x^2y^2/5x^4y^2. Thank you.
To simplify the expression (40x^2y^2)/(5x^4y^2) using none negative exponents, we can follow these steps:
Step 1: Divide the numerical coefficients.
40/5 = 8
Step 2: Divide the variables with the same base (x) by subtracting their exponents.
x^2 / x^4 = x^(2-4) = x^(-2)
Step 3: Divide the variables with the same base (y) by subtracting their exponents.
y^2 / y^2 = y^(2-2) = y^0
Step 4: Simplify any terms with an exponent of 0.
Since any non-zero number raised to the power of 0 is equal to 1, y^0 = 1.
Putting it all together, the simplified expression becomes:
8x^(-2) * 1
= 8/x^2
Therefore, the expression (40x^2y^2)/(5x^4y^2), written using none negative exponents, simplifies to 8/x^2.