a. Simplify, your answer should contain no exponents. 12^-5 * 12^7 b. Using complete sentences, explain the steps to simplify this problem.

Answer 1

a. To simplify \( 12^{-5} \times 12^{7} \), we can use the properties of exponents. Specifically, when multiplying terms with the same base, we add the exponents.

1. Start with the expression \( 12^{-5} \times 12^{7} \).
2. Recall the property of exponents: \( a^m \times a^n = a^{m+n} \).
3. Here, our base \( a \) is 12, \( m = -5 \), and \( n = 7 \).
4. Add the exponents: \[ -5 + 7 = 2. \]
5. Now rewrite the expression using the result from the addition of the exponents: \[ 12^{-5} \times 12^{7} = 12^{2}. \]
6. Finally, convert \( 12^{2} \) to its numerical form: \[ 12^{2} = 144. \]

So, the simplified expression is \( 144 \).

b. To simplify the expression \( 12^{-5} \times 12^{7} \), I started by identifying the common base, which is 12. According to the rules of exponents, when multiplying terms with the same base, we need to add the exponents together. In this case, the exponents are -5 and 7. I added these values, resulting in \( -5 + 7 \), which equals 2. This means that the expression simplifies to \( 12^{2} \). Finally, to express this without exponents, I calculated \( 12^{2} \) as \( 12 \times 12 = 144 \). Thus, the simplified answer is \( 144 \).

Answer 2

Make this shorter please

Answer 3

a. To simplify \( 12^{-5} \times 12^{7} \):

1. Use the property of exponents: \( a^m \times a^n = a^{m+n} \).
2. Here, add the exponents: \( -5 + 7 = 2 \).
3. This gives us \( 12^{2} \), which equals \( 144 \).

So, the simplified expression is \( 144 \).

b. To simplify \( 12^{-5} \times 12^{7} \), I added the exponents (-5 and 7) to get 2. Thus, the expression simplifies to \( 12^{2} \), which equals \( 144 \). The final answer is \( 144 \).