Question

Find the numerical equivalent of 8^9 x 8^-6. can you do it like a 8th grader pleases

Answer 1

can you dumb it down please

Answer 2

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:

\[
\boxed{512}
\]

Answer 3

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!