Simplify. Express your answer using exponents.
(10^8 m^4 n^5)^4
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Simplify. Express your answer using exponents. (10^8 m^4 n^5)^4 Submit
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To simplify the expression ((10^8 m^4 n^5)^4), you will use the power of a power rule, which states that ((a^m)^n = a^{m cdot n}).
Here’s how to apply it step-by-step:
1. Raise each term inside the parentheses to the power of 4:
[
(10^8)^4, (m^4)^4, (n^5)^4
]
2. Apply the power of a power rule:
[
(10^8)^4 = 10^{8 cdot 4} = 10^{32}
]
[
(m^4)^4 = m^{4 cdot 4} = m^{16}
]
[
(n^5)^4 = n^{5 cdot 4} = n^{20}
]
3. Combine all the results:
[
10^{32} m^{16} n^{20}
]
Therefore, the simplified expression is (10^{32} m^{16} n^{20}).