Question

Simplify 2x multiplied by x^(-1/2)

(the above is x to the power of minus a half)

Answer 1

`2√(x)`

Explanation:

`\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^(b+c)`

`2x \cdot x^{-(1)/(2)} = 2x^{1-(1)/(2)} = 2x^{(1)/(2)} = 2√(x)`

Another way of doing this is to see that

`x^{-(1)/(2)} = (1)/(√(x) )`

So
`2x \cdot x^{-(1)/(2)} = (2x)/(√(x) ) =2√(x)`