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2 Find the quotient. Write your answer using exponents. \( \frac{8^{12}}{8^{6}} \)

Ask by Rodriquez Bowers. in the United States
Mar 07,2025

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Answer

The quotient is \( 8^6 \).

Solution

We are given the quotient \[ \frac{8^{12}}{8^{6}} \] Since the bases are the same (both are 8), we subtract the exponents according to the law \[ \frac{a^m}{a^n} = a^{m-n} \] Thus, \[ \frac{8^{12}}{8^{6}} = 8^{12-6} = 8^6 \] So, the quotient is \[ \boxed{8^6} \]

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The Deep Dive

To find the quotient \( \frac{8^{12}}{8^{6}} \), you can use the properties of exponents. When dividing like bases, you subtract the exponents: \( 8^{12} ÷ 8^{6} = 8^{12-6} = 8^{6} \). So the answer is \( 8^{6} \). Now, if you're curious, the power of exponents can be likened to a magic spell in math—make it easier to handle large numbers! Instead of writing out \( 8 \) multiplied by itself 12 times or 6 times, you can just say "I cast the spell, and here's my answer!" Learning this property can definitely simplify your calculations. Plus, if you ever take algebra or higher math courses, exponents will be your best friends! They show up everywhere—from calculus to science equations. So mastering them now will pave the way for future success.

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