Simplify $9 m^3 y^2 \div 3 m^2 y$
Answer (1)
Rewrite the division as a fraction: 3 m 2 y 9 m 3 y 2 .
Divide the coefficients: 3 9 = 3 .
Simplify the powers of m : m 2 m 3 = m .
Simplify the powers of y : y y 2 = y .
Combine the simplified terms: The simplified expression is 3 m y .
Explanation
Understanding the problem We are asked to simplify the expression $9 m^3 y^2
div 3 m^2 y$. This involves dividing terms with exponents.
Rewriting as a fraction First, rewrite the division as a fraction: 3 m 2 y 9 m 3 y 2 This makes it easier to see how to simplify the expression.
Dividing the coefficients Next, divide the coefficients: 3 9 = 3 So, the coefficient of the simplified expression will be 3.
Simplifying powers of m Now, simplify the powers of m :
m 2 m 3 = m 3 − 2 = m 1 = m When dividing terms with the same base, we subtract the exponents.
Simplifying powers of y Similarly, simplify the powers of y :
y y 2 = y 2 − 1 = y 1 = y Again, we subtract the exponents.
Combining the terms Finally, combine the simplified terms: 3 c d o t m c d o t y = 3 m y So, the simplified expression is 3 m y .
Final Answer Therefore, the simplified form of $9 m^3 y^2
div 3 m^2 y$ is 3 m y .
Examples
In real life, simplifying expressions like this can help in various scenarios. For example, if you are calculating the volume of a rectangular prism with dimensions that are expressed algebraically, simplifying the expression can make it easier to find the volume. Also, in physics, when dealing with formulas involving multiple variables, simplifying expressions can make calculations more manageable and help in understanding the relationships between different quantities. This skill is also useful in computer programming when optimizing code for efficiency.
