Apply the product rule of integer exponents to find the numerical equivalent of%C2%A0%C2%A0 12−5⋅127 . Show your work and explain how you used the product rule of integer exponents.(2 points)
To apply the product rule of integer exponents, we need to multiply the base (12) by itself the number of times indicated by the exponent (-5⋅127).
First, let's break it down and simplify the expression inside the parentheses: -5⋅127. This means that we need to multiply -5 by 127.
Next, let's multiply 12 by itself the number of times indicated by the simplified exponent (-5⋅127). Since the exponent is negative, we need to take the reciprocal of the base raised to the positive exponent.
The reciprocal of 12^(-5⋅127) is the same as (1/12)^(5⋅127).
Therefore, the numerical equivalent is (1/12)^(5⋅127) × -5 × 127.
We can now calculate the numerical value using a calculator or a software program.
To apply the product rule of integer exponents, we multiply the base and add the exponents.
Let's break down the expression step by step:
We have 12^-5 * 127.
Using the product rule, we know that when multiplying two exponents with the same base, we add the exponents.
First, let's simplify 12^-5:
Since the base is 12, we keep the base the same and add the exponents. -5 + 0 = -5. So, 12^-5 becomes (1/12^5).
Now, let's rewrite the expression:
(1/12^5) * 127.
Next, we can apply the product rule by multiplying the numerators and the denominators:
(1 * 127) / (12^5).
Simplifying further:
127 / (12^5).
Finally, we can evaluate the expression by calculating the power of 12:
(127 / 248,832).
The numerical equivalent of the expression 12^-5 * 127 is approximately 0.00051.
To apply the product rule of integer exponents, we need to understand the rule itself. The product rule states that when multiplying two numbers with the same base, we can add their exponents.
In this case, we have 12^(-5) * 12^7. Both terms have the same base of 12, so we can rewrite the expression using the product rule as 12^(-5 + 7).
Now, let's simplify it step by step:
First, let's simplify the exponent -5 + 7.
-5 + 7 = 2.
Now, we have 12^2. This means we need to multiply 12 by itself twice:
12 * 12 = 144.
Therefore, 12^(-5) * 12^7 is equal to 144.
To summarize, we used the product rule of integer exponents by adding the exponents of the same base (12) to simplify the expression. This allowed us to obtain the numerical equivalent of 144.