Question

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 of integer exponents.

Answer 1

whtas the answer

Answer 2

now put it in a sintcen

Answer 3

To find the numerical equivalent of the expression \( 12^{-5} \cdot 12^7 \), we can apply the product rule of integer exponents. The product rule states that when multiplying two powers with the same base, we add the exponents.

The product rule can be expressed as:

\[
a^m \cdot a^n = a^{m+n}
\]

In our case, the base \( a \) is \( 12 \), \( m \) is \( -5 \), and \( n \) is \( 7 \). Applying the product rule:

\[
12^{-5} \cdot 12^7 = 12^{-5 + 7}
\]

Now, we perform the addition of the exponents:

\[
-5 + 7 = 2
\]

So, we have:

\[
12^{-5} \cdot 12^7 = 12^2
\]

Next, we calculate \( 12^2 \):

\[
12^2 = 12 \cdot 12 = 144
\]

Therefore, the numerical equivalent of \( 12^{-5} \cdot 12^7 \) is:

\[
\boxed{144}
\]

Answer 4

The numerical equivalent of the expression \( 12^{-5} \cdot 12^7 \) is \( 144 \).

Answer 5

The numerical equivalent of the expression \( 12^{-5} \cdot 12^7 \) is \( 144 \).