Question
Simplify this expression using exponent rules five to the second power times five to the ninth power and parentheses times five to the zero power equals what
Answers
GPT-4o mini
To simplify the expression \(5^2 \cdot 5^9 \cdot (5^0)\), we can use the exponent rules.
1. **Applying the product of powers rule:** When multiplying with the same base, you add the exponents:
\[
5^2 \cdot 5^9 = 5^{2+9} = 5^{11}
\]
2. **Using the fact that \(5^0 = 1\):**
\[
5^{11} \cdot 5^0 = 5^{11} \cdot 1 = 5^{11}
\]
Thus, the simplified expression is:
\[
5^{11}
\]
1. **Applying the product of powers rule:** When multiplying with the same base, you add the exponents:
\[
5^2 \cdot 5^9 = 5^{2+9} = 5^{11}
\]
2. **Using the fact that \(5^0 = 1\):**
\[
5^{11} \cdot 5^0 = 5^{11} \cdot 1 = 5^{11}
\]
Thus, the simplified expression is:
\[
5^{11}
\]