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

Answer 1

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 2

can you dumb it down please

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!