Simplify The numerical equivalent of 12^−5⋅12^7, we can apply the product rule of integer exponents. By adding the exponents, we simplify the expression to 12^2, and the numerical equivalent is 144.

Question

The numerical equivalent of 12^(-5) * 12^7 using the product rule of integer exponents, you can combine the two expressions by adding their exponents. The product rule states that when you multiply two expressions with the same base, you can add their exponents:

12^(-5) * 12^7 = 12^(-5 + 7)

Now, simplify the exponent:

12^(-5 + 7) = 12^2

12^2 means 12 raised to the power of 2, which is equal to 144.

So, 12^(-5) * 12^7 is equivalent to 144. Here's the explanation of how we used the product rule:

1. We had two expressions with the same base, 12.

2. We applied the product rule by adding the exponents, (-5) and 7, which gave us 2.

3. Finally, we simplified 12^2 to 144 to find the numerical equivalent.

Therefore, 12^(-5) * 12^7 equals 144.

Now, we can simplify -5+7 to get 2. Our expression becomes 122. Since any number raised to the power of 2 is equal to the number multiplied by itself, we can calculate the numerical equivalent of this expression by performing 12 * 12, which equals 144.

Therefore, the numerical equivalent of 12−5⋅127 is 144.

Answer 1

Your explanation of the numerical equivalent of \( 12^{-5} \cdot 12^{7} \) is correct! Here’s a concise breakdown of the steps:

1. Product Rule of Exponents: When you multiply expressions with the same base, you add the exponents. \[ 12^{-5} \cdot 12^{7} = 12^{-5 + 7} \]

2. Simplify the Exponents: \[ -5 + 7 = 2 \] So, \[ 12^{-5 + 7} = 12^{2} \]

3. Calculate \( 12^2 \): \[ 12^2 = 12 \cdot 12 = 144 \]

In conclusion, the numerical equivalent of \( 12^{-5} \cdot 12^{7} \) is indeed \( 144 \). Great job summarizing the process!