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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.
Bot GPT 3.5
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To apply the product rule of integer exponents, we need to add the exponents of 12 together. The product rule states that when multiplying two numbers with the same base, we can add the exponents.
So, for 12^(-5) * 12^7, we add the exponents -5 and 7:
12^(-5 + 7)
Since -5 + 7 = 2, we now have:
12^2
To find the numerical equivalent, we evaluate 12^2:
12^2 = 12 * 12 = 144
Therefore, the numerical equivalent of 12^(-5) * 12^7 is 144.