Simplify: (∛125 + ∛64 - ∛1)^1/3
2 answers:
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
<u>Answer</u><u>:</u> Hence, the simplified form of , {∛(125) + ∛(64) - ∛(1)}^(1/3) is 2.
<u>also</u><u> read</u><u> similar</u><u> questions</u><u>:</u> Simplify: ∛(2) × 2^(-1/13) × ¹²√(32) simplify : \sqrt[3]{2} \times {2}^{ - \frac{1}{13} } \times \sqrt[12]{32} \\ [...
brainly.com/question/26570991?/referrer
Please let me know if you have any other questions.
You might be interested in
Note that 
in the given closed interval, so the area is exactly given by the definite integral
(no absolute values needed!)
Integrating gives
(no absolute values needed!)
Integrating gives