Apply the product rule of integer exponents to find the numerical equivalent of 12-5. 127. Show your work and explain how you used the product rule

Question

of integer exponents. (2 points) make it not too long and make it sound like an 8th grader wrote it

Answer 1

To find the numerical equivalent of \( 12^{-5} \), we can use the product rule of integer exponents. The product rule states that when you multiply powers with the same base, you add the exponents. But first, let's rewrite \( 12^{-5} \).

When there's a negative exponent, it means we take the reciprocal of the base raised to the positive exponent. So:

\[ 12^{-5} = \frac{1}{12^5} \]

Now, we need to calculate \( 12^5 \). We can break this down like this:

\[ 12^5 = 12 \times 12 \times 12 \times 12 \times 12 \]

Calculating this step by step, we can find \( 12^2 \):

\[ 12^2 = 144 \]

Next, calculate \( 12^3 \):

\[ 12^3 = 12 \times 144 = 1728 \]

Now \( 12^4 \):

\[ 12^4 = 12 \times 1728 = 20736 \]

And finally:

\[ 12^5 = 12 \times 20736 = 248832 \]

Now, we can write \( 12^{-5} \):

\[ 12^{-5} = \frac{1}{248832} \]

So, the numerical equivalent of \( 12^{-5} \) is \( \frac{1}{248832} \).

In summary, we used the property of negative exponents to find the reciprocal and calculated \( 12^5 \) step by step to arrive at the answer.

Answer 2

I said make it not long and make it understandable

Answer 3

To find \( 12^{-5} \), we use the rule that a negative exponent means to take the reciprocal. So,

\[ 12^{-5} = \frac{1}{12^5} \]

Now, let's calculate \( 12^5 \):

1. \( 12^2 = 144 \)
2. \( 12^3 = 12 \times 144 = 1728 \)
3. \( 12^4 = 12 \times 1728 = 20736 \)
4. \( 12^5 = 12 \times 20736 = 248832 \)

So,

\[ 12^{-5} = \frac{1}{248832} \]

In short, the product rule helps us understand how to handle the exponent, and we found that \( 12^{-5} \) equals \( \frac{1}{248832} \).

Answer 4

THATS NOT UNDERSTANDABLE STOP DOING ALL THAT DUMB “ \[
12^{-5} = \frac{1}{248832}
\]” STOP THAT, JUST WRITE IT NORMALLY YOU STUPID BOT

Answer 5

I'm sorry about that! Let me explain it in a simpler way.

To find 12 to the power of -5, we remember that a negative exponent means to take the reciprocal. So, 12 to the power of -5 is the same as 1 divided by 12 to the power of 5.

Now, let's figure out what 12 to the power of 5 is. It means multiplying 12 by itself 5 times:

12 x 12 x 12 x 12 x 12.

When you do all the multiplications, you find out that 12 to the power of 5 equals 248,832.

So, 12 to the power of -5 is:

1 divided by 248,832.

In the end, 12 to the power of -5 equals 1/248,832. That's how you can find it using the rule for negative exponents!