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
The product rule of integer exponents states that for any integers a and b, and any positive integer n:
a^m * a^n = a^(m+n)
In this problem, we have 12^(-5) * 12^7. According to the product rule, we can add the exponents:
(-5) + 7 = 2
So, 12^(-5) * 12^7 is equivalent to 12^2.
Now, we need to calculate the numerical value of 12^2. To do this, we multiply 12 by itself:
12^2 = 12 * 12 = 144
Therefore, the numerical equivalent of 12^(-5) * 12^7 is 144.