Answer:
[tex]7\sqrt6[/tex]
Step-by-step explanation:
The original expression is [tex]6^{\frac{1}{2}} + 6^{\frac{3}{2}}[/tex]
The last one is a trick answer: [tex]6^{\frac{1}{2}} 6^{\frac{3}{2} }= 6^{\frac{3}{4}}[/tex] i.e. the exponents are added when the two are multiplied and the base of the exponent is the same(in this case 6)
[tex]6^{\frac{1}{2} }= \sqrt{6} \\6^{\frac{3}{2} } = (6^{\frac{1}{2} })^3 = (\sqrt{6} )^3\\[/tex]
So [tex]6^{\frac{1}{2}} + 6^{\frac{3}{2}} = \sqrt{6} + (\sqrt{6} )^3[/tex]
Factoring out [tex]\sqrt{6}[/tex] in the above equation gives [tex]\sqrt{6} [1 + (\sqrt{6})^2]\\\\[/tex]
But [tex](\sqrt{6} )^2 = 6[/tex] square of a square root of a number is the number
So the expression becomes [tex]\sqrt{6} (1 + 6) = 7\sqrt6[/tex]
