Simplify d^6/d^7 and express your answer using positive exponents.
Understand the Problem
The question is asking us to simplify the expression d^6/d^7 using the division rule for exponents. We need to apply the rule that states when dividing like bases, we subtract the exponents.
Answer
The simplified expression is \( \frac{1}{d} \).
Answer for screen readers
The simplified expression is ( \frac{1}{d} ).
Steps to Solve
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Identify the bases and exponents Here we have the base ( d ) with exponents 6 and 7 in the expression ( \frac{d^6}{d^7} ).
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Apply the division rule for exponents According to the rule, when dividing like bases, we subtract the exponents: $$ \frac{d^a}{d^b} = d^{a-b} $$ In our case, ( a = 6 ) and ( b = 7 ).
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Subtract the exponents Perform the subtraction: $$ 6 - 7 = -1 $$ So, we have: $$ d^{6-7} = d^{-1} $$
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Express with positive exponents To express the answer with a positive exponent, we rewrite ( d^{-1} ) as: $$ \frac{1}{d^1} = \frac{1}{d} $$
The simplified expression is ( \frac{1}{d} ).
More Information
When you divide terms with the same base, you can simplify by subtracting the exponents. The result can often show a negative exponent, which can then be rewritten as a fraction to reflect positive exponents.
Tips
- Forgetting the negative exponent rule: It's crucial to remember that exponents can be negative and must be converted to positive form when required.
- Mistaking subtraction: Double-check that you subtract the exponents correctly.
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