Mathematics

Problem

Let

A = 6^{\frac{3}{7}}

and

B = 2^{\frac{5}{7}} \times 3^{\frac{5}{7}}

. a. (i) Simplify

B

so that it is expressed as a single power of 6. b. (ii) Without numerical approximation, compare

A

and

B

and state which is greater. c. (iii) Using your result from part (ii), compare

A^{7}

and

B^{7}

and explain your reasoning.