Divide $20 a^5 b^3$ by $5 a^2 b$.
Answer (1)
Divide the coefficients: 20/5 = 4 .
Divide the powers of a : a 5 / a 2 = a 5 − 2 = a 3 .
Divide the powers of b : b 3 / b = b 3 − 1 = b 2 .
Combine the results: 4 a 3 b 2 .
Explanation
Understanding the Problem We are asked to divide 20 a 5 b 3 by 5 a 2 b . This involves dividing the coefficients and applying the rules of exponents for the variables a and b .
Dividing the Coefficients First, we divide the coefficients: 5 20 = 4
Dividing the Powers of a Next, we divide the powers of a . Recall that when dividing powers with the same base, we subtract the exponents: a 2 a 5 = a 5 − 2 = a 3
Dividing the Powers of b Now, we divide the powers of b , again subtracting the exponents: b b 3 = b 3 − 1 = b 2
Combining the Results Finally, we combine the results to get the final answer: 4 a 3 b 2
Examples
Understanding how to divide expressions with exponents is useful in many areas, such as calculating the volume of a rectangular prism. For example, if the volume of a prism is 20 a 5 b 3 and the area of the base is 5 a 2 b , then dividing the volume by the base area gives the height of the prism, which is 4 a 3 b 2 . This skill is also crucial in simplifying complex algebraic expressions and solving equations in physics and engineering.
