Apply the product rule of integer exponents to find the numerical equivalent of 12 ^ - 5 * 12 ^ 7
To apply the product rule of integer exponents, we add the exponents when multiplying two numbers with the same base.
So, to find the numerical equivalent of 12^-5 * 12^7, we can combine the exponents:
12^-5 * 12^7 = 12^(-5 + 7)
= 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 can use the rule which states that when we multiply two numbers with the same base, we add their exponents. Here's how to calculate it step by step:
Step 1: Understand the product rule of integer exponents:
The product rule states that when multiplying two numbers with the same base, you can add their exponents. In other words, for any number a and any integers m and n, a^m * a^n = a^(m + n).
Step 2: Identify the base:
The base of both terms in your expression is 12.
Step 3: Apply the product rule:
12^-5 * 12^7 can be simplified using the product rule. Since both terms have the same base of 12, we can add their exponents:
12^(-5 + 7)
Step 4: Evaluate the sum of the exponents:
-5 + 7 equals 2. Therefore, we can simplify the expression as follows:
12^2
Step 5: Evaluate the expression:
To find the numerical equivalent of 12^2, simply multiply 12 by itself:
12 * 12 = 144
Therefore, the numerical equivalent of 12^-5 * 12^7 is 144.
To apply the product rule of integer exponents, you need to add the exponents when the bases are the same. In this case, the base is 12.
First, let's rewrite the expression:
12^(-5) * 12^7
The product rule states:
a^m * a^n = a^(m+n)
Now, let's apply the product rule to our expression:
12^(-5) * 12^7 = 12^((-5) + 7)
Simplifying the exponent:
12^((-5) + 7) = 12^2
Calculating the result:
12^2 = 12 * 12 = 144
Therefore, the numerical equivalent of 12^(-5) * 12^7 is 144.