Apply the product rule of intiger exponents to find the numerical equivalent of 12^-5•12^7. Show your work and explain how you used the product rule of intiger exponents.
The product rule of integer exponents states that when multiplying two terms with the same base, we add their exponents.
To find the numerical equivalent of 12^-5 • 12^7, we can first apply the product rule to simplify the expression.
12^-5 • 12^7 = 12^(-5 + 7)
Since the bases are the same (12), we add the exponents (-5 + 7) which gives us 12^2.
Therefore, 12^-5 • 12^7 is numerically equivalent to 12^2.
To calculate 12^2, we multiply 12 by itself:
12^2 = 12 × 12 = 144.
Hence, 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 add the exponents together because they have the same base.
The product rule states that when you multiply two numbers with the same base, you simply add the exponents.
So, in this case, we have:
12^-5 • 12^7
Applying the product rule, we add the exponents:
12^(-5 + 7)
Simplifying further:
12^2
Therefore, the numerical equivalent of 12^-5 • 12^7 is 12^2.
To calculate the final result, we raise the base, which is 12, to the power of 2:
12^2 = 12 × 12 = 144.
Hence, 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 use the property that states: x^m • x^n = x^(m+n), where x represents the base and m, n are integers.
Now let's break down the steps:
Step 1: Begin by multiplying the coefficients.
12^-5 • 12^7 = 12^(-5+7)
Step 2: Apply the product rule of integer exponents.
12^(-5+7) = 12^2
Step 3: Simplify the expression.
12^2 = 144
Therefore, the numerical equivalent of 12^-5 • 12^7 is 144.
Explanation:
The product rule of integer exponents states that when you multiply two terms with the same base, you can combine their exponents by adding them together. In this case, we have 12^-5 • 12^7.
First, we simplify the coefficients by multiplying them, which gives us 12^(-5+7).
Then, we use the product rule of integer exponents by adding -5 and 7 together, which gives us 2. So, 12^(-5+7) becomes 12^2.
Finally, we simplify 12^2 to get the numerical equivalent, which is 144.