Question

MEDAL::What is the simplified form of the seventh root of x to the fifth power times the seventh root of x to the fifth power? how do i solve this???

Answer 1

Remember
(x^m)(x^n)=x^(m+n)

and
$\sqrt[n]{x^m} =x^{ \frac{m}{n} }$ so


$(\sqrt[7]{x^5})(\sqrt[7]{x^5})$ =
$(x^{ \frac{5}{7})(x^{ \frac{5}{7}) }$ =
$x^(\frac{5}{7}+\frac{5}{7})$ =
 $x^(\frac{10}{7})$=
$(x^ \frac{7}{7} )(x^ \frac{3}{7})$=
(x)($x^ \frac{3}{7}$=
$x \sqrt[7]{x^3}$

Answer 2

The mathematical expression of the given above is,
                           (x^1/7)^5  x   (x^17)^5
Take note that for (x^n)^m, the answer is x^nm. For our expression above,
                                      (x^5/7)   x (x^5/7)
Another rule for exponent is that for (x^n) x (x^m) the answer would be x^(n + m). For the expression,
                                                x^10/7