Step-by-step explanation:
Given that: {∛(125) + ∛(64) - ∛(1)}^(1/3)
= {∛(5 * 5 * 5) + ∛(4 * 4* 4) -∛(1)}^(1/3)
= {∛(5³) + ∛(4³) - ∛(1)}^(1/3)
[since, ⁿ√(a) = a^(1/n)]
= {(5³)^(1/3) + (4³)^(1/3) - (1)^(1/3)}^(1/3)
[since, (aᵐ)ⁿ = aᵐⁿ}
= {(5)^{3*(1/3)} + (4)^{3*(1/3)} - (1*1*1)}^(1/3)
= {{5)^1 + (4)^1 - 1}^(1/3)
= (5 + 4 -1)^(1/3)
= (9 - 1)^(1/3)
= 8^(1/3)
= (2*2*2)^(1/3)
= (2³)^(1/3)
[since, (aᵐ)ⁿ = aᵐⁿ]
= (2)^{3*(1/3)}
= (2)¹
= 2
Therefore, {∛(125) + ∛(64) - ∛(1)}^(1/3) = 2
Answer: Hence, the simplified form of , {∛(125) + ∛(64) - ∛(1)}^(1/3) is 2.
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