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.
The product rule of integer exponents states that when multiplying two numbers with the same base, we add their exponents.
In this problem, we have 12 raised to the power of -5 multiplied by 12 raised to the power of 7. Since the base is the same (12), we can apply the product rule of integer exponents.
12^-5 x 12^7 = 12^(-5 + 7)
Now, we can calculate the sum of the exponents:
12^(-5 + 7) = 12^2
Since 12 raised to the power of 2 is equal to 144, the numerical equivalent of 12^-5 x 12^7 is 144.
To find the numerical equivalent of the expression 12^-5 • 12^7, we can use the product rule of integer exponents.
According to the product rule of exponents, when multiplying two expressions with the same base, we can add their exponents.
So, here's how we can solve the expression step-by-step:
Step 1: Apply the product rule and add the exponents:
12^-5 • 12^7 = 12^(-5 + 7)
Step 2: Simplify the exponent:
12^(-5 + 7) = 12^2
Step 3: Evaluate the expression:
12^2 = 144
Therefore, the numerical equivalent of 12^-5 • 12^7 is 144.
To apply the product rule of integer exponents to find the numerical equivalent of 12^-5 • 12^7, we need to understand what the product rule states. The product rule states that when multiplying two numbers with the same base, we can keep the base the same and add the exponents together.
So, let's break down the given expression and apply the product rule:
12^-5 • 12^7
The product rule states that when we multiply two numbers with the same base, we add the exponents. In this case, the base is 12, and the exponents are -5 and 7.
Applying the product rule, we add the exponents:
12^(-5 + 7)
Simplifying further:
12^2
The expression 12^2 is equivalent to 12 multiplied by itself, which equals 144. Therefore, the numerical equivalent of 12^-5 • 12^7 is 144.
In summary, we applied the product rule of integer exponents by adding the exponents when multiplying two numbers with the same base. We simplified the expression by adding -5 and 7 to get 2, and then evaluated 12^2, which resulted in the numerical value of 144.