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

To apply the product rule of integer exponents, we need to remember that it states:

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

In this case, we have 12^(-5) * 127.

Using the product rule of integer exponents, we can rewrite this expression as:

1/(12^5) * 127

Now let's simplify each term separately:

12^5 = 12 * 12 * 12 * 12 * 12 = 248,832

So, 1/(12^5) = 1/248,832.

Now, we can substitute this value back into the original expression:

1/248,832 * 127

To calculate this, we simply need to divide 127 by 248,832:

127/248,832 ≈ 0.00051

Therefore, the numerical equivalent of 12^(-5) * 127 is approximately 0.00051.