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.