To divide $x^3 y$ by $x^4 y$, first divide $y$ by $y$ to get $x^3 / x^4$. Which of these would you do next to solve?
A. $x^{(3 \div 4)}$
B. $x^{(4-3)}$
C. $x^{(4 \cdot 3)}$
D. $x^{(3-4)}$
Answer (1)
To simplify x 4 y x 3 y , we first divide y by y to get x 4 x 3 . Then, using the quotient of powers rule, x b x a = x a − b , we simplify x 4 x 3 to x 3 − 4 . Therefore, the next step is x ( 3 − 4 ) .
Explanation
Simplifying the Expression We are given the expression x 4 y x 3 y . The first step is to divide y by y , which results in x 4 x 3 . We need to determine the next step to simplify this expression.
Applying the Quotient of Powers Rule To simplify x 4 x 3 , we use the quotient of powers rule, which states that x b x a = x a − b . In this case, a = 3 and b = 4 . Therefore, x 4 x 3 = x 3 − 4 .
Identifying the Correct Option Now we compare our result, x 3 − 4 , with the given options:
x ( 3 ÷ 4 )
x ( 4 − 3 )
x ( 4 ⋅ 3 )
x ( 3 − 4 )
The correct option is x ( 3 − 4 ) .
Examples
Understanding how to simplify expressions with exponents is crucial in many areas, such as physics and engineering. For example, when calculating the force between two charged particles, the formula involves dividing by the square of the distance between them. Simplifying such expressions using exponent rules makes calculations easier and more accurate. Imagine you are calculating the gravitational force between two planets; you'll need to simplify expressions with exponents to find the correct force value. This skill is also essential in computer science when analyzing algorithms and data structures.
