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 use the power of a product rule, which states that ((ab)^n = a^n b^n) and also the rule ( (x^m)^n = x^{m cdot n} ).
1. First, let’s distribute the exponent (3) to each term inside the parentheses:
[
(5s^5 t^6 u^5)^3 = 5^3 (s^5)^3 (t^6)^3 (u^5)^3
]
2. Now calculate each term:
– (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:
[
125s^{15} t^{18} u^{15}
]
So, the simplified expression is:
[
boxed{125s^{15} t^{18} u^{15}}
]
This represents the correct simplification using exponents! If you have any more questions or need further