begin{aligned}
sqrt[3]{4^{x+1}} &= 2sqrt{8^{x}} \
sqrt[3]{2^{x+1}} &= 2sqrt{2^{3x}} \
2^{frac{2x+2}{3}}&= 2(2^{frac{3}{2}x}) \
2^{frac{2x+2}{3}}&= 2^{1+frac{3}{2}x} \
frac{2x+2}{3} &= 1+frac{3}{2}x \
4x+4 &= 6+9x \
5x &= -1\
x&=-frac{1}{5}
end{aligned}

JAWAB : B

begin{aligned}
4^{x}-4^{x-1} &= 6 &rightarrow 4^{x}-frac{4^{x}}{4}&=6 \
3times 4^{x} &= 24 &rightarrow 4^{x}&=8 \
2^{2x}&= 2^{3} &rightarrow x&=frac{3}{2} \
end{aligned}
jadi, $(2x)^{x} = (3)^{frac{3}{2}}=3times 3^{frac{1}{2}}=3sqrt{3}$

JAWAB : B

begin{aligned}
frac{sqrt[3]{4^{5-x}}}{8} &= frac{1}{2x+1}Leftrightarrow frac{2^{frac{10-2x}{3}}}{2^{3}} = 2^{-2x-1} \
2^{frac{10-2x}{3}-3} &= 2^{-2x-1} \
frac{10-2x}{3} – 3&= -2x-1 \
10-2x-9 &=-6-3 \
4x &= -4Leftrightarrow x=-1
end{aligned}

JAWAB : B

$a+bsqrt{5}=frac{frac{1}{2}-frac{1}{5}}{frac{1}{2}+frac{1}{sqrt{5}}}=frac{frac{sqrt{5}-2}{2sqrt{5}}}{frac{sqrt{5}+2}{2sqrt{5}}}=frac{sqrt{5}-2}{5-4}$

Rasionalkan penyebutnya

begin{flalign}
a+bsqrt{5}&= frac{sqrt{5}-2}{sqrt{5}-2}times frac{sqrt{5}-2}{sqrt{5}-2}=frac{9-4sqrt{5}}{5-4} &\
a+bsqrt{5}&= 9-4sqrt{5} &\
end{flalign}

begin{flalign}
text {Jadi nilai a = 9 dan b = -4,} &\
text {Sehingga a+b = 9+(-4) = 5} &\
end{flalign}

JAWAB : B

begin{aligned}
frac{(a^{frac{5}{3}}b^{frac{1}{2}}-a^{frac{2}{2}}b^{frac{3}{2}})}{(a^{frac{7}{2}}b^{frac{1}{2}}-a^{frac{3}{2}}b)}= frac{b^{frac{1}{2}}a^{frac{2}{3}}\(a-b)}{ a^{frac{2}{3}}b^{frac{1}{2}}\(sqrt{a}+sqrt{b})} \
= frac{(sqrt{a}+sqrt{b})(sqrt{a}-sqrt{b})}{ (sqrt{a}-sqrt{b})} = sqrt{a}+sqrt{b}
end{aligned}

JAWAB : B

begin{flalign}
r & = frac{20sqrt{2} – 25}{(10+20sqrt{2})(2-sqrt{2})} \
& = frac{5(4sqrt{2} – 5)}{10(1+2sqrt{2})(2-sqrt{2})} , , , , , , , text{(bagi 5)} &\
& = frac{(4sqrt{2} – 5)}{2(1+2sqrt{2})(2-sqrt{2})} , , , , , , , text{(kalikan penyebutnya)} &\
& = frac{(4sqrt{2} – 5)}{2(3sqrt{2} – 2)} , , , , , , , text{(kalikan sekawan)} &\
& = frac{(4sqrt{2} – 5)}{2(3sqrt{2} – 2)} . frac{3sqrt{2} + 2}{3sqrt{2} + 2} &\
& = frac{14 – 7sqrt{2}}{2(9.2- 4 )} = frac{7(2 – sqrt{2})}{2.14} = frac{(2 – sqrt{2})}{4}
end{flalign}

Menentukan nilai $(4r-2)^2$

begin{flalign}
(4r-2)^2 & = left( 4.frac{(2 – sqrt{2})}{4} – 2 right)^2 &\
& = left( (2 – sqrt{2}) – 2 right)^2 &\
& = left( – sqrt{2} right)^2 &\
& = 2
end{flalign}

JAWAB : D

begin{flalign}
& dfrac{left(sqrt{3}+sqrt{7} right)left( sqrt{3}-sqrt{7} right)}{2sqrt{5}-4sqrt{2}} &\
& = dfrac{3-7}{2 left( sqrt{5}-2sqrt{2} right) } times dfrac{sqrt{5}+2sqrt{2}}{sqrt{5}+2sqrt{2}} &\
& = dfrac{-4 left( sqrt{5} + 2sqrt{2} right)}{2 left( 5- 8 right) } &\
& = dfrac{-4 left( sqrt{5} + 2sqrt{2} right)}{-6} \

& = dfrac{2}{3} left( sqrt{5} + 2sqrt{2} right) &\
end{flalign}

JAWAB : A

begin{flalign}
& dfrac{5 left( sqrt{3}+sqrt{2} right)left( sqrt{3}-sqrt{2} right)^{3}}{left( 2sqrt{2}-sqrt{3} right)} &\
& = dfrac{5 left( sqrt{3}+sqrt{2} right)left( sqrt{3}-sqrt{2} right)left( sqrt{3}-sqrt{2} right)^{2}}{left( 2sqrt{2}-sqrt{3} right)} &\
& = dfrac{5 left( 3-2 right)left( sqrt{3}-sqrt{2} right)^{2}}{left( 2sqrt{2}-sqrt{3} right)} &\
& = dfrac{5 left( 3+2-2sqrt{6} right)}{left( 2sqrt{2}-sqrt{3} right)} &\
& = dfrac{25-10sqrt{6}}{left( 2sqrt{2}-sqrt{3} right)} times dfrac{left( 2sqrt{2}+sqrt{3} right)}{left( 2sqrt{2}+sqrt{3} right)} &\
& = dfrac{50sqrt{2}+25sqrt{3}-20sqrt{12}-10sqrt{18}}{left( 8-3 right)} &\
& = dfrac{50sqrt{2}+25sqrt{3}-40sqrt{3}-30sqrt{2}}{5} &\
& = dfrac{20sqrt{2}-15sqrt{3}}{5} &\
& = 4sqrt{2}-3sqrt{3}
end{flalign}

JAWAB : E

begin{flalign}
3^{2x+3} &=sqrt[3]{27^{x+5}} &\
3^{2x+3} &=27^{dfrac{x+5}{3}} &\
3^{2x+3} &=(3^{3})^{dfrac{x+5}{3}} &\
3^{2x+3} &=3^{x+5} &\
& Rightarrow 2x+3=x+5 &\
& Rightarrow 2x-x=5-3 &\
& Rightarrow x=2
end{flalign}

JAWAB : E

begin{flalign}
sqrt{8^{3-x}} &= 4 cdot 2^{1-2x} &\
8^{dfrac{3-x}{2}} &= 2^{2} cdot 2^{1-2x} &\
2^{ dfrac{3(3-x)}{2}} &= 3-2x &\
9-3x &= 6-4x &\
4x-3x &= 6-9 &\
x &= -3 &\
1- x &= 1-(-3) =4
end{flalign}

JAWAB : E