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Evaluate (1256)−58.\large \left(\frac{1}{256} \right)^{-\frac{5}{8 }}.(2561)−85.
If a>0 a>0 a>0, simplify
(a23+a−13)3+(a23−a−13)3. \left( a^{\frac{2}{3}} + a^{-\frac{1}{3}} \right)^3 + \left( a^{\frac{2}{3}} - a^{-\frac{1}{3}} \right)^3. (a32+a−31)3+(a32−a−31)3.
Evaluate
(2+3−2−3)13. \left( \sqrt{2 + \sqrt{3}} - \sqrt{2 - \sqrt{3}} \right)^{\frac13}. (2+3−2−3)31.
If x=315+3−152 x = \dfrac{3^{\frac{1}{5}} + 3^{ -\frac{1}{5}} }{2} x=2351+3−51, evaluate
(x+x2−1)10. \left( x + \sqrt{x^2 - 1} \right)^{10}. (x+x2−1)10.
Suppose that aaa and bbb satisfy 12×2413+8113+6×(3×215)13=ab3,12 \times 24^{\frac{1}{3}}+81^{\frac{1}{3}}+6 \times \left(3 \times 2^{15}\right)^{\frac{1}{3}}=a \sqrt[3]{b},12×2431+8131+6×(3×215)31=a3b, where bbb is a prime number. What is a+ba+ba+b?
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