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 of integer exponents.
The product rule of integer exponents states that when you multiply two terms with the same base, you add their exponents. In this case, we have 12^-5 * 12^7.
To apply the product rule, we add the exponents together: -5 + 7 = 2.
So, 12^-5 * 12^7 is equivalent to 12^2.
Now let's find the numerical value of 12^2. 12^2 means we multiply 12 by itself, twice:
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 can combine the two expressions into one by adding the exponents together. The product rule states that when you multiply two terms with the same base, you can simply add their exponents.
First, let's write out the expression: 12^-5 * 12^7.
Now, applying the product rule, we can add the exponents:
12^(-5+7)
To simplify the exponent further, we can add -5 and 7:
12^2
Finally, we calculate the expression:
12^2 = 12 * 12 = 144
Therefore, the numerical equivalent of 12^-5 * 12^7 is 144.
To apply the product rule of integer exponents, we can multiply the bases and add the exponents. The product rule states that for any positive integers m and n, and any real number b, b^m * b^n = b^(m + n).
In this case, we have 12^(-5) * 12^7, where the base is 12. To find the numerical equivalent, we can use the product rule as follows:
12^(-5) * 12^7 = 12^(-5 + 7)
First, let's simplify the exponents:
-5 + 7 = 2
Now, substitute the simplified exponent back into the equation:
12^(-5 + 7) = 12^2
So the numerical equivalent of 12^(-5) * 12^7 is 12^2.
To evaluate 12^2, simply multiply 12 by itself:
12^2 = 12 * 12 = 144
Therefore, the numerical equivalent of 12^(-5) * 12^7 is 144.
In summary, we used the product rule of integer exponents to simplify the expression. By adding the exponents together, we combined the two terms into a single term with an exponent of 2. Then, we evaluated the expression by multiplying the base 12 by itself, resulting in the final answer of 144.