apply the product rule of integer exponents to find the numerical equivalent to 12 to the power of -5 times 12 to the power of 7. show your work and explain how you used the product rule of integer exponents.
The product rule of integer exponents states that when multiplying two numbers with the same base, we add the exponents.
First, let's rewrite 12 to the power of -5 as 1/12^5.
So, we have (1/12^5) * 12^7.
Now, using the product rule of integer exponents, we add the exponents to get 12^7-5.
12^7-5 = 12^2.
Therefore, the numerical equivalent is 12^2, which is equal to 144.
To find the numerical equivalent of \(12^{-5} \times 12^7\) using the product rule of integer exponents, we need to add the exponents.
The product rule states that when you multiply two numbers with the same base, you add their exponents.
Let's break it down step-by-step:
Step 1: Start with the expression \(12^{-5} \times 12^7\).
Step 2: Apply the product rule of integer exponents. Add the exponents of the same base, which is 12, to get a single exponent: \((-5) + 7 = 2\).
Step 3: Rewrite the expression with the new exponent: \(12^2\).
Step 4: Calculate the numerical value of \(12^2\), which is \(12 \times 12 = 144\).
Therefore, the numerical equivalent of \(12^{-5} \times 12^7\) is 144.
To apply the product rule of integer exponents, we need to multiply the bases (in this case, 12) and add the exponents. The product rule of integer exponents states that when multiplying two exponential expressions with the same base, you can add the exponents together.
Let's break it down step by step:
Step 1: Start with the expression 12^(-5) * 12^7
Here, we have two exponential expressions with the same base, which is 12.
Step 2: Apply the product rule by adding the exponents:
12^(-5) * 12^7 can be rewritten as 12^((-5) + 7).
Step 3: Simplify the exponents:
(-5) + 7 = 2
Step 4: Rewrite the expression with the simplified exponent:
12^2
Step 5: Calculate the numerical value:
12^2 = 12 * 12 = 144
So, the numerical equivalent of 12^(-5) * 12^7 is 144.