Simplify. Express your answer using exponents. (5s^5 t^6 u^5)^3

To simplify the expression ((5s^5 t^6 u^5)^3), we will apply the power of a product rule, which states that ((ab)^n = a^n b^n), and the power of a power rule, which states that ((x^m)^n = x^{mn}).

1. Start by applying the exponent to each part of the product:

[

(5s^5 t^6 u^5)^3 = 5^3 (s^5)^3 (t^6)^3 (u^5)^3

]

2. Now, calculate each part:

– (5^3 = 125)

– ((s^5)^3 = s^{5 cdot 3} = s^{15})

– ((t^6)^3 = t^{6 cdot 3} = t^{18})

– ((u^5)^3 = u^{5 cdot 3} = u^{15})

3. Putting it all together gives us:

[

125s^{15} t^{18} u^{15}

]

So, the simplified expression is:

[

boxed{125s^{15} t^{18} u^{15}}

]

This is now fully simplified and expressed using exponents! If you need further assistance or have more questions, feel free to ask!