Simplify r^0 / r^-6. Express your answer using positive exponents.
Understand the Problem
The question is asking to simplify the expression r^0 / r^-6 using positive exponents. It involves applying the laws of exponents to achieve this.
Answer
The simplified expression is $r^6$.
Answer for screen readers
The simplified expression is $r^6$.
Steps to Solve
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Identify the problem You need to simplify the expression $\frac{r^0}{r^{-6}}$.
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Apply the exponent rule for zero The rule states that any non-zero number raised to the power of zero is 1. Thus, $r^0 = 1$.
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Rewrite the expression using positive exponents Using the property of negative exponents, $r^{-n} = \frac{1}{r^n}$, we can rewrite the denominator: $$\frac{r^0}{r^{-6}} = \frac{1}{r^{-6}} = r^6$$
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Final expression The simplified form using only positive exponents is: $$ r^6 $$
The simplified expression is $r^6$.
More Information
Using the laws of exponents simplifies the expression effectively. Remember that $r^0$ equals 1, and negative exponents indicate reciprocal relationships.
Tips
- Confusing $r^0$ as being other than 1.
- Misapplying the negative exponent rule, leading to incorrect simplification.
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