i need help solving this problem. what is the power of x. (squareroot of x over the fifth root of x) all to the power of 1/3

Guest Aug 19, 2015

#1**+5 **

Square root of x ---> x^{1/2}

Fifth root of x ---> x^{1/5}

( x^{1/2} / x^{1/5} )^{1/3}

Since inside the parentheses is a division problem, subtract the exponents:

1/2 - 1/5 = 3/10:

= ( x^{3/10} )^{1/3}

Since this is an exponent to an exponent, multiply the exponents:

= x^{3/10 x 1/3} = x^{1/10} or the tenth root of x

geno3141 Aug 19, 2015

#1**+5 **

Best Answer

Square root of x ---> x^{1/2}

Fifth root of x ---> x^{1/5}

( x^{1/2} / x^{1/5} )^{1/3}

Since inside the parentheses is a division problem, subtract the exponents:

1/2 - 1/5 = 3/10:

= ( x^{3/10} )^{1/3}

Since this is an exponent to an exponent, multiply the exponents:

= x^{3/10 x 1/3} = x^{1/10} or the tenth root of x

geno3141 Aug 19, 2015