Apply the product rule of integer exponents to find the numerical equivalent of 12−5⋅127

Question

. Show your work and explain how you used the product rule of integer exponents.(2 points)
in a small paraghraph

Answer 1

To solve the expression \( 12^{-5} \cdot 12^7 \) using the product rule of integer exponents, we first recall that the product rule states that when multiplying two expressions with the same base, we can add their exponents.

In this case, we have the base \( 12 \) with exponents \( -5 \) and \( 7 \). Applying the product rule, we combine the exponents:

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

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

\[ 12^2 = 144 \]

Thus, the numerical equivalent of \( 12^{-5} \cdot 12^{7} \) is \( 144 \). By applying the product rule, we simplified the expressions and combined the exponents to arrive at this final result.