Question
Describe how to simplify the expression \( \frac{3^{-6}}{3^{-4}} \). Divide the bases and then add the exponents. Keep the base the same and then add the exponents. Multiply the bases and then subtract the exponents. Keep the base the same and then subtract the exponents.
Ask by Mann O'Quinn. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Keep the base the same and then subtract the exponents.
Solution
When dividing exponential expressions with the same base, you subtract the exponent in the denominator from the exponent in the numerator. For the expression (3⁻⁶)/(3⁻⁴), you would do the following:
1. Keep the base the same (which is 3).
2. Subtract the exponent in the denominator from the exponent in the numerator: -6 - (-4) = -6 + 4 = -2.
3. The simplified expression is 3⁻².
So, the correct method is: Keep the base the same and then subtract the exponents.
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Simplify this solution Beyond the Answer
To simplify the expression \( \frac{3^{-6}}{3^{-4}} \), you can apply the property of exponents that states when dividing two powers with the same base, you subtract the exponents. So, \( 3^{-6} \div 3^{-4} = 3^{-6 - (-4)} = 3^{-6 + 4} = 3^{-2} \). This is how you get to the final answer! Now, for a little historical fun: the laws of exponents were formalized in mathematics quite a bit after the concept of exponentiation was introduced in the 16th century. Mathematicians like René Descartes and John Wallis helped shape how we understand these operations today. So next time you’re crunching numbers, you can appreciate the centuries of math wisdom that brought us here!
