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