How does ((sqrt(64, 5)*2^-1/5)/sqrt(8))^-4 equal 4? I've tried so many methods and can't seem to arrive to that answer (yes, I have to show how I worked it out). Any help is greatly appreciated!
+33661 Try it as follows:
Numerator
sqrt(64,5) → sqrt(2*32,5) → sqrt(2,5)*sqrt(32,5) → sqrt(2,5)*sqrt(2^5,5) → sqrt(2,5)*2
sqrt(2,5) is 2^(1/5), so sqrt(64,5) → 2*2^(1/5)
Hence sqrt(64,5)*2^(-1/5) → 2*2^(1/5)*2^(-1/5) → 2
Denominator
sqrt(8) → (sqrt(2)*sqrt(4)) → 2*sqrt(2)
Numerator/Denominator → 1/sqrt(2)
Raise this to the power -4: (1/sqrt(2))^-4 → sqrt(2)^4 → (sqrt(2)^2)^2 → 2^2 → 4
+33661 Try it as follows:
Numerator
sqrt(64,5) → sqrt(2*32,5) → sqrt(2,5)*sqrt(32,5) → sqrt(2,5)*sqrt(2^5,5) → sqrt(2,5)*2
sqrt(2,5) is 2^(1/5), so sqrt(64,5) → 2*2^(1/5)
Hence sqrt(64,5)*2^(-1/5) → 2*2^(1/5)*2^(-1/5) → 2
Denominator
sqrt(8) → (sqrt(2)*sqrt(4)) → 2*sqrt(2)
Numerator/Denominator → 1/sqrt(2)
Raise this to the power -4: (1/sqrt(2))^-4 → sqrt(2)^4 → (sqrt(2)^2)^2 → 2^2 → 4
