Question
Find the numerical equivalent of 8^9 x 8^-6. can you do it like a 8th grader pleases
Answers
Answered by
GPT-4o mini
Sure! To solve \( 8^9 \times 8^{-6} \), we can use the rules of exponents.
When you multiply two numbers with the same base (in this case, 8), you add their exponents. The rule is:
\[
a^m \times a^n = a^{m+n}
\]
So let's add the exponents:
\[
8^9 \times 8^{-6} = 8^{9 + (-6)} = 8^{9 - 6} = 8^{3}
\]
Now we just need to find \( 8^3 \):
\[
8^3 = 8 \times 8 \times 8
\]
First, calculate \( 8 \times 8 \):
\[
8 \times 8 = 64
\]
Now, multiply that result by 8:
\[
64 \times 8 = 512
\]
So, the numerical equivalent of \( 8^9 \times 8^{-6} \) is:
\[
\boxed{512}
\]
When you multiply two numbers with the same base (in this case, 8), you add their exponents. The rule is:
\[
a^m \times a^n = a^{m+n}
\]
So let's add the exponents:
\[
8^9 \times 8^{-6} = 8^{9 + (-6)} = 8^{9 - 6} = 8^{3}
\]
Now we just need to find \( 8^3 \):
\[
8^3 = 8 \times 8 \times 8
\]
First, calculate \( 8 \times 8 \):
\[
8 \times 8 = 64
\]
Now, multiply that result by 8:
\[
64 \times 8 = 512
\]
So, the numerical equivalent of \( 8^9 \times 8^{-6} \) is:
\[
\boxed{512}
\]
Answer
can you dumb it down please
Answered by
GPT-4o mini
Of course! Let’s break it down step by step in a simple way.
1. **Start with the problem**: We have \( 8^9 \times 8^{-6} \).
2. **What do the numbers mean?** The "8" is the base, and the numbers (9 and -6) are the exponents. The exponent tells us how many times to multiply the base by itself.
3. **Rule for multiplying**: When you multiply two numbers with the same base, you add the exponents. So for \( 8^9 \times 8^{-6} \):
- You add \( 9 \) and \( -6 \).
\[
9 + (-6) = 3
\]
4. **Now we have a simpler problem**: We can change our original problem to:
\[
8^3
\]
5. **Calculating \( 8^3 \)**: This means we multiply 8 by itself three times:
\[
8 \times 8 \times 8
\]
- First, calculate \( 8 \times 8 = 64 \).
- Then, multiply that result by 8: \( 64 \times 8 = 512 \).
6. **Final answer**: So, \( 8^9 \times 8^{-6} \) equals **512**.
The final answer is:
\[
\boxed{512}
\]
I hope this step-by-step explanation makes it clearer!
1. **Start with the problem**: We have \( 8^9 \times 8^{-6} \).
2. **What do the numbers mean?** The "8" is the base, and the numbers (9 and -6) are the exponents. The exponent tells us how many times to multiply the base by itself.
3. **Rule for multiplying**: When you multiply two numbers with the same base, you add the exponents. So for \( 8^9 \times 8^{-6} \):
- You add \( 9 \) and \( -6 \).
\[
9 + (-6) = 3
\]
4. **Now we have a simpler problem**: We can change our original problem to:
\[
8^3
\]
5. **Calculating \( 8^3 \)**: This means we multiply 8 by itself three times:
\[
8 \times 8 \times 8
\]
- First, calculate \( 8 \times 8 = 64 \).
- Then, multiply that result by 8: \( 64 \times 8 = 512 \).
6. **Final answer**: So, \( 8^9 \times 8^{-6} \) equals **512**.
The final answer is:
\[
\boxed{512}
\]
I hope this step-by-step explanation makes it clearer!