Question

Question #c2af6

Answer 1

`35x^6`

Explanation:

`color(blue)((49x^6)^(1/2)xx(125x^9)^(1/3)`

To solve this we use three rules

`o. color(brown)((xy)^z=z^zy^z`

`o. color(brown)((x^y)^z=x^(yz)`

`o. color(brown)(x^yxxx^z=x^(y+z)`

So, lets find the solution

`rarr(49x^6)^(1/2)xx(125x^9)^(1/3)`

Use `color(brown)((xy)^z=z^zy^z`

`rarr(49)^(1/2)xx(x^6)^(1/2)xx(125)^(1/3)xx(x^9)^(1/3)`

`rarr(7xx7)^(1/2)xx(x^6)^(1/2)xx(5xx5xx5)^(1/3)xx(x^9)^(1/3)`

`rarr(7^2)^(1/2)xx(x^6)^(1/2)xx(5^3)^(1/3)xx(x^9)^(1/3)`

Use `color(brown)((x^y)^z=x^(yz)`

`rarr(7)^((2)(1/2))xx(x)^((6)(1/2))xx(5)^((3)(1/3))xx(x)^((9)(1/3))`

`rarr7xxx^3xx5xxx^3`

Use `color(brown)(x^yxxx^z=x^(y+z)`

`color(green)(rArr35x^6`

Hope this helps!!! ☺☻