Apply the product rule of integer exponents to find the numerical equivalant of 12^-5 times 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 terms with the same base but different exponents, you can add the exponents.
In this case, we have 12^(-5) multiplied by 12^7. Since the base is the same (12), we can use the product rule to simplify the expression.
When we add the exponents -5 and 7, we get 2:
(-5) + 7 = 2
Therefore, 12^(-5) multiplied by 12^7 is equal to 12^2.
To find the numerical value of 12^2, we need to evaluate it:
12^2 = 12 x 12 = 144
So, the numerical equivalent of 12^(-5) times 12^7 is 144.
To find the numerical equivalent of 12^-5 times 12^7 using the product rule of integer exponents, we can follow these steps:
Step 1: Recall the product rule of integer exponents, which states that to multiply two powers with the same base, you keep the base the same and add the exponents:
a^m * a^n = a^(m + n)
Step 2: Apply the product rule to the given problem.
12^-5 * 12^7 = 12^(-5 + 7)
Step 3: Simplify the exponent expression (-5 + 7) = 2.
12^2
Step 4: Calculate the numerical value of 12^2.
12^2 = 144
Therefore, the numerical equivalent of 12^-5 times 12^7 is 144.
To apply the product rule of integer exponents to find the numerical equivalent of 12^-5 times 12^7, we need to understand the rule first.
The product rule states that when multiplying two exponential expressions with the same base, we add the exponents. Mathematically, it can be expressed as:
a^m * a^n = a^(m + n),
where "a" is the base, and "m" and "n" are the exponents.
Now, let's solve the problem step by step and demonstrate the application of the product rule:
Step 1: Write down the given expressions:
12^-5 * 12^7
Step 2: Apply the product rule by adding the exponents:
12^(-5 + 7)
Step 3: Simplify the exponent:
12^2
Step 4: Evaluate the expression:
12^2 = 144
Therefore, the numerical equivalent of 12^-5 times 12^7 is 144.