Simplify. Express your answer using exponents. (10^8 m^4 n^5)^4 Submit

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}).