$\frac{5 x^7 y^5}{10 x y^3}$
Answer (1)
Simplify the numerical coefficients: 10 5 = 2 1 .
Simplify the x terms: x x 7 = x 6 .
Simplify the y terms: y 3 y 5 = y 2 .
Combine the simplified terms: 2 1 x 6 y 2 .
Explanation
Understanding the Problem We are asked to simplify the expression 10 x y 3 5 x 7 y 5 . This involves simplifying the numerical coefficients and using the rules of exponents to simplify the variable terms.
Simplifying Coefficients First, let's simplify the numerical coefficients: 10 5 = 2 1 .
Simplifying x terms Next, we simplify the expression involving x . Using the rule x b x a = x a − b , we have x x 7 = x 7 − 1 = x 6 .
Simplifying y terms Now, we simplify the expression involving y . Using the rule y b y a = y a − b , we have y 3 y 5 = y 5 − 3 = y 2 .
Combining Terms Finally, we combine the simplified terms to get the final simplified expression: 2 1 x 6 y 2 .
Examples
Simplifying expressions like this is useful in many areas of math and science. For example, if you are calculating the area of a shape with variable dimensions, you might end up with an expression like the one we just simplified. Simplifying it makes it easier to understand how the area changes as the dimensions change. Also, in physics, you might encounter similar expressions when dealing with forces or velocities.
