Apply the product rule of exponents to find the numerical equivalent of 12^-5 x 12^7. Show your work and explain how you used the product rule of integer exponents
The product rule of exponents states that when multiplying two numbers with the same base, you add the exponents. In other words, a^m * a^n = a^(m+n).
In this case, we have 12^-5 * 12^7. Since the base, 12, is the same, we can apply the product rule of exponents.
First, we add the exponents: (-5) + 7 = 2.
So, 12^-5 * 12^7 can be simplified to 12^2.
To find the numerical equivalent of 12^2, we simply calculate 12^2 as follows:
12^2 = 12 * 12 = 144.
Therefore, the numerical equivalent of 12^-5 * 12^7 is 144.
To apply the product rule of exponents, we use the formula: a^m x a^n = a^(m+n), where "a" represents the base and "m" and "n" are the exponents.
Given the expression 12^(-5) x 12^7, we can combine the terms using the product rule:
12^(-5) x 12^7 = 12^((-5) + 7)
First, let's simplify the exponent:
(-5) + 7 = 2
So, we have:
12^(-5) x 12^7 = 12^2
Now, we can calculate the numerical equivalent of 12^2:
12^2 = 12 x 12 = 144
Therefore, the numerical equivalent of 12^(-5) x 12^7 is 144.
To find the numerical equivalent of 12^-5 x 12^7 using the product rule of exponents, we can follow these steps:
Step 1: Understand the Product Rule of Exponents
The product rule of exponents states that when multiplying two numbers with the same base, we can add their exponents together while keeping the base the same. Mathematically, it can be represented as a^m x a^n = a^(m + n).
Step 2: Apply the Product Rule
In this case, we have 12^-5 x 12^7. Since the base is the same (12), we can combine the exponents using the product rule. Therefore, the expression becomes 12^(-5 + 7).
Step 3: Calculate the Result
To simplify the expression, we add the exponents of 12, which gives us 12^2. Mathematically, it can be calculated as follows: (-5 + 7) = 2. Therefore, the numerical equivalent of 12^-5 x 12^7 is 12^2.
Step 4: Simplify the Result
To further simplify 12^2, we calculate the value of 12 raised to the power of 2. That equals 144. Hence, the numerical equivalent of 12^-5 x 12^7 is 144.
In summary, by applying the product rule of exponents, we added the exponents of 12 to find the exponent of the result. We then calculated 12^2, which resulted in 144 as the final answer.