$\frac{6 x^6 y^4}{2 x^2 y^2} =$
F $3 x^4 y^2$
G $3 x^3 y^2$
H $4 x^3 y^2$
J $4 x^4 y^2$
K None of these
Answer (1)
Divide the coefficients: 2 6 = 3 .
Subtract the exponents of x : x 6 − 2 = x 4 .
Subtract the exponents of y : y 4 − 2 = y 2 .
The simplified expression is 3 x 4 y 2 .
Explanation
Understanding the problem We are asked to simplify the expression 2 x 2 y 2 6 x 6 y 4 and choose the correct answer from the given options.
Simplifying the expression To simplify the expression, we need to divide the coefficients and subtract the exponents of the corresponding variables.
Dividing the coefficients First, divide the coefficients: 2 6 = 3 .
Subtracting the exponents of x Next, subtract the exponents of x : x 6 − 2 = x 4 .
Subtracting the exponents of y Then, subtract the exponents of y : y 4 − 2 = y 2 .
Combining the results Therefore, the simplified expression is 3 x 4 y 2 .
Choosing the correct option Comparing the simplified expression 3 x 4 y 2 with the given options, we see that it matches option F.
Final Answer Thus, the correct answer is 3 x 4 y 2 .
Examples
Understanding how to simplify expressions with exponents is crucial in many areas, such as calculating the area or volume of geometric shapes. For instance, if you have a rectangular prism with dimensions 2 x 2 , 3 x 2 y , and y , the volume would be 2 x 2 × 3 x 2 y × y = 6 x 4 y 2 . Simplifying such expressions helps in determining the overall size or capacity of objects in engineering and design.
