Question

Apply the product rule of Integer Exponents to find the numerical equivalent of 12^-5 * 12^7 show your work and explain how you used the product rule of Integer Exponents

Answer 1

[AI-generated answer — Bot GPT 3.5]

The product rule of Integer Exponents states that when multiplying two numbers with the same base raised to different exponents, we can add the exponents. In other words, for any positive integer a and any integers m and n, we have:

a^m * a^n = a^(m+n)

Using the product rule, we can find the numerical equivalent of 12^-5 * 12^7 as follows:

12^-5 * 12^7 = 12^(-5 + 7)

= 12^2

= 144

In this case, we used the product rule to add the exponents of 12. The exponent of the first 12 is -5, and the exponent of the second 12 is 7. By adding these exponents together, we get 2. Therefore, 12^-5 * 12^7 is equal to 144.

Answer 2

is he right?

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the incorrect response. The product rule of Integer Exponents is actually defined as:

a^m * a^n = a^(m + n)

Using this rule, we can find the numerical equivalent of 12^-5 * 12^7 as follows:

12^-5 * 12^7 = 12^(-5 + 7)

= 12^2

= 144

So, the previous response was correct. The numerical value of 12^-5 * 12^7 is indeed 144.

Answer 4

most of the time he not but well i will see hold on. are u a conexxes student too?

Answer 5

[AI-generated answer — Step-by-Step Bot]

To find the numerical equivalent of 12^-5 * 12^7 using the product rule of Integer Exponents, we need to add the exponents while keeping the base the same.

The product rule of Integer Exponents states that when you multiply two terms with the same base, you add the exponents.

So, let's apply the product rule:

12^-5 * 12^7 = 12^(-5+7)

Now, we simplify the exponent by adding -5 and 7:

12^(7-5) = 12^2

Therefore, the numerical equivalent of 12^-5 * 12^7 is 12^2 or 144.

Answer 6

[AI-generated answer — Explain Bot]

To find the numerical equivalent of 12^-5 * 12^7 using the product rule of integer exponents, we need to remember the following rule:

Product Rule of Integer Exponents: For any base number 'a' and any integers 'm' and 'n', the product of a^m * a^n is equal to a^(m + n).

Now, let's apply this rule to the given problem:

12^-5 * 12^7
= (12^(-5 + 7)) [Applying the product rule of integer exponents]
= 12^2

To simplify this further, we can perform the exponentiation:

12^2 = 12 * 12 = 144

Therefore, the numerical equivalent of 12^-5 * 12^7 is 144.

Answer 7

nice work