Simplify q^-8 * r * q^-1 * r^0. Express your answer as a single term, without any additional formatting.
Understand the Problem
The question is asking to simplify the expression involving exponents and to express the answer as a single term without any additional formatting.
Answer
$q^{-9} r$
Answer for screen readers
$q^{-9} r$
Steps to Solve
-
Identify the expression
We have the expression:
$$ q^{-8} \cdot r \cdot q^{-1} \cdot r^{0} $$ -
Simplify (r^{0})
Recall that any non-zero number raised to the power of zero equals 1. Thus,
$$ r^{0} = 1 $$
This allows us to simplify the expression to:
$$ q^{-8} \cdot r \cdot q^{-1} $$ -
Combine the (q) terms
Using the property of exponents that states (a^m \cdot a^n = a^{m+n}), we can combine (q^{-8}) and (q^{-1}):
$$ q^{-8} \cdot q^{-1} = q^{-8 + (-1)} = q^{-9} $$
So, our expression now becomes:
$$ q^{-9} \cdot r $$ -
Final expression
The final simplified expression is:
$$ q^{-9} \cdot r $$
$q^{-9} r$
More Information
This result shows the combined effect of multiplying the terms with exponents. It emphasizes the importance of understanding exponent rules, especially how to handle negative exponents and multiplication.
Tips
- Forgetting that (r^{0} = 1) and including it in the final expression.
- Not combining the (q) terms correctly according to exponent rules.
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