Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.
(x^[1/2]) / (x^[5/4] * x^[-2])

Question

anonymous · Answer

sqrt(x) / [ fourthroot(x^5) * x^-2 ] ...

anonymous · Answer

= sqrt(x) / [ fourthroot(x^5) / x^2 ] = sqrt(x) / [ ( fourthroot(x^5) / 1 ) * 1/(x^2) ] = sqrt(x) / [ fourthroot(x^5) / x^2 ] = ... ?

anonymous · Answer

ultimately simplifies to x^(5/4). just need to realize how to get that answer.

ranga · Answer

$$\frac{ \sqrt{x} }{ \sqrt[4]{x^5} * x^{-2}} = \frac{ x^{1/2} }{ x^{5/4} * x^{-2} } = \frac{ x^{1/2} * x^2 }{ x^{5/4} }$$

ranga · Answer

$$= \frac{ x^{1/2+2} }{ x^{5/4} } = \frac{ x^{5/2} }{ x^{5/4} } = x^{5/2-5/4} = x^{5/4}$$

anonymous · Answer

7x^2+9x+8=0

ranga · Answer

7x^2 + 9x + 8 = 0 
$$\Large x = \frac{ -b \pm \sqrt{b ^{2} - 4ac} }{ 2(7) } = \frac{ -9 \pm \sqrt{9 ^{2} - 4(7)(8)} }{ 14 }$$ $$\Large x = \frac{ -9 \pm \sqrt{-143} }{ 14 } = \frac{ -9}{14} + \frac{\sqrt{143} }{ 14 }i \quad or \quad \frac{ -9}{14} - \frac{\sqrt{143} }{ 14 }i $$