Simplify square root of 2 multiplied by the cube root of 2. a 2 to the power of 1 over 6 b 2 to the power of 2 over 3 c2 to the power of 5 over 6 d2 to the power of 7 over 6

Square-root of two multiplied by the cube-root of 2
=sqrt(2)*(2)^(1/3)
=2^(1/2)*2^(1/3)
=2^(1/2+1/3)     multiplication rule of exponents
=2^((3+2)/6)
=2^(5/6)
=(2^5)^(1/6)sixth root of 2^5
=(32)^(1/6) sixth root of 32.