Write an expression for the sequence of operations described below. Raise the difference of q and r to the 3rd power. Do not simplify any part of the expression.
Understand the Problem
The question is asking us to write a mathematical expression based on a sequence of operations that involves two variables, q and r. Specifically, it instructs to find the difference between q and r, and then raise that difference to the third power. The emphasis is on not simplifying the expression.
Answer
$(q - r)^3$
Answer for screen readers
The expression for the operations described is $(q - r)^3$.
Steps to Solve
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Identify the operation: difference We need to find the difference between the two variables, $q$ and $r$. The mathematical expression for the difference is given by: $$ q - r $$
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Apply the next operation: raise to the third power Next, we need to raise the difference obtained in Step 1 to the third power. This can be expressed as: $$ (q - r)^3 $$
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Write the final expression The final expression that represents the operation of raising the difference to the third power is: $$ (q - r)^3 $$
The expression for the operations described is $(q - r)^3$.
More Information
Raising an expression to the power of three means multiplying it by itself three times. The expression $(q - r)^3$ is a perfect representation of the operation as specified.
Tips
- Simplifying the expression: Some may try to simplify $(q - r)^3$ further, but the problem explicitly states not to simplify.
- Incorrectly applying the power: Ensure that the parentheses are used correctly when indicating the base for exponentiation.
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