Question
Simplify expression, using exponent rules and parentheses five to the eighth power times five to the -3 power and parentheses to the fourth power
Answers
GPT-4o mini
To simplify the expression \( (5^8 \cdot 5^{-3})^4 \), we can follow these steps using the exponent rules.
1. **Combine the exponents**: When multiplying with the same base, we add the exponents.
\[
5^8 \cdot 5^{-3} = 5^{8 + (-3)} = 5^{8 - 3} = 5^5
\]
2. **Raise to the fourth power**: Now we need to raise \( 5^5 \) to the fourth power. When raising a power to another power, we multiply the exponents.
\[
(5^5)^4 = 5^{5 \cdot 4} = 5^{20}
\]
Thus, the simplified expression is:
\[
\boxed{5^{20}}
\]
1. **Combine the exponents**: When multiplying with the same base, we add the exponents.
\[
5^8 \cdot 5^{-3} = 5^{8 + (-3)} = 5^{8 - 3} = 5^5
\]
2. **Raise to the fourth power**: Now we need to raise \( 5^5 \) to the fourth power. When raising a power to another power, we multiply the exponents.
\[
(5^5)^4 = 5^{5 \cdot 4} = 5^{20}
\]
Thus, the simplified expression is:
\[
\boxed{5^{20}}
\]