$\frac{10 p^4}{6 p}$
Answer (1)
Rewrite the expression as a product of fractions: 6 10 × p p 4 .
Simplify the numerical fraction: 6 10 = 3 5 .
Simplify the variable fraction using the quotient rule for exponents: p p 4 = p 3 .
Combine the simplified parts to get the final answer: 3 5 p 3 .
Explanation
Understanding the Problem We are given the expression 6 p 10 p 4 and asked to simplify it.
Rewriting the Expression First, we can rewrite the expression as a product of fractions: 6 p 10 p 4 = 6 10 × p p 4 .
Simplifying the Numerical Fraction Now, we simplify the numerical fraction 6 10 by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 6 10 = 6 ÷ 2 10 ÷ 2 = 3 5 .
Simplifying the Variable Fraction Next, we simplify the variable fraction p p 4 . Using the quotient rule for exponents, which states that a n a m = a m − n , we have: p p 4 = p 1 p 4 = p 4 − 1 = p 3 .
Combining the Results Finally, we combine the simplified numerical fraction and the simplified variable fraction to obtain the simplified expression: 3 5 × p 3 = 3 5 p 3 .
Final Answer Therefore, the simplified expression is 3 5 p 3 .
Examples
Simplifying expressions like this is useful in many areas of math and science. For example, if you are calculating the volume of a cylinder with a changing radius, you might end up with an expression like this that needs to be simplified to make further calculations easier. It also helps in understanding the relationship between different variables in an equation.
