Answer:
roots and powers are opposites like plus and minus or multiply and divide.
the square root of a power (meaning a root symbol with no other number like root 3 for example) is just 2÷ the power or yroot ÷ power
[tex] \sqrt{250} = 15.81139[/tex]
[tex] \sqrt{ {x}^{16} } = {x}^{8} [/tex]
root by it self means 2 so power 16 ÷power 2 = power 8
[tex] \sqrt{x} = {x}^{ \frac{1}{2} } [/tex]
therefore
[tex] \frac{ \sqrt{ {250x}^{16} } }{ \sqrt{2x} } = \frac{ {15.81139x}^{8} }{ {x}^\frac{1}{2} } [/tex]
simplify
opposite of fraction (aka divide ) is multiply
[tex] \frac{ {15.81139x}^{8} }{ {x}^{ \frac{1}{2} } } \times {x}^{ \frac{1}{2} } = {15.81139x}^{8} \times {x}^{2} [/tex]
You multiply by x^1/2 to cancel on one side of equation. what you do to the left you have to do to the right so the x^1/2 stays unaffected on right.
to multiply a fraction you simply swap numerator and denominator, therefore 1/2 becomes 2/1 but you simply express as just 2 for short
power x power is the same as xpower + xpower
[tex] {x}^{8} \times {x}^{2} = {x}^{10} [/tex]
[tex] {15.81139x}^{10} [/tex]
multiplying powers is just like addition
