Question

Which of the following is equal to the square root of the cube root of 2?

2 to the power of 2 over 3
2 to the power of 3 over 2
2 to the power of 1 over 3
2 to the power of 1 over 6
http://prntscr.com/bsv2qi

Answer 1

First change the cube root into a 1/3 exponent \[\large \sqrt{ \sqrt[3]{2} } = \sqrt{2^{1/3}}\]then the square root into a 1/2\[\large \sqrt{2^{1/3}} = \left( 2^{1/3} \right)^{1/2}\]Then just apply the exponent rule (multiply the exponents)