To apply the product rule of integer exponents to find the numerical equivalent of 12^(-5) * 127, we first need to understand the rule.
The product rule of integer exponents states that when multiplying numbers with the same base but different exponents, you can add the exponents and keep the base the same.
In this case, we have 12^(-5) * 127. The base is 12 and the exponents are -5 and 1.
Using the product rule of integer exponents, we add the exponents:
12^(-5) * 127 = 12^(-5+1) * 127
Since -5+1 equals -4, we can rewrite the expression as:
12^(-5) * 127 = 12^(-4) * 127
Now, to find the numerical equivalent, we calculate 12^(-4):
12^(-4) = 1 / 12^4 = 1 / 20736 = 0.000048
Now we can multiply this result by 127:
0.000048 * 127 = 0.006096
Therefore, the numerical equivalent of 12^(-5) * 127 is 0.006096.
By applying the product rule of integer exponents, we were able to simplify the expression and find the numerical value.
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.(2 points)
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