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 you multiply two numbers with the same base, you can add their exponents.
To find the numerical equivalent of 12^-5 * 12^7, we first apply the product rule by adding the exponents of 12. The base is the same, which is 12.
12^-5 * 12^7 = 12^(-5 + 7)
Next, we simplify the exponent:
12^(-5 + 7) = 12^2
Finally, we calculate the numerical value of 12^2, which is:
12^2 = 144
Therefore, 12^-5 * 12^7 is equal to 144.
The product rule of integer exponents states that when you multiply two exponents with the same base, you can add their exponents.
So, let's apply the product rule to find the numerical equivalent of 12^-5 * 12^7:
Step 1: Rewrite the expression using the product rule:
12^-5 * 12^7 = 12^(-5 + 7)
Step 2: Simplify the exponent by adding the exponents:
12^(-5 + 7) = 12^2
Step 3: Calculate the numerical value of 12^2:
12^2 = 12 * 12 = 144
Therefore, the numerical equivalent of 12^-5 * 12^7 is 144.
To find the numerical equivalent of 12^-5 * 12^7 using the product rule of integer exponents, we need to understand the rule and then apply it.
The product rule of integer exponents states that when multiplying two terms with the same base, you can add their exponents:
a^m * a^n = a^(m + n)
In this case, the base is 12, and we have 12^-5 and 12^7. According to the rule, we can add the exponents:
12^-5 * 12^7 = 12^(-5 + 7)
Now, we need to simplify the exponents:
(-5 + 7) = 2
Therefore, 12^-5 * 12^7 is equivalent to 12^2.
To calculate the numerical value of 12^2, we multiply 12 by itself:
12 * 12 = 144
Therefore, 12^-5 * 12^7 = 12^2 = 144.