Question

1.(root 3/5 )^x+1 =125/27

2. Find the value of 64^-1/3(64^1/3-64^2/3)

3. root 50+^2/₃ =(0.6)^2-3x find x4.

Answer 1

$1.(\frac{\sqrt{3}}{\sqrt{5}}{)}^{x+1}=\frac{125}{27}=\frac{5^3}{3^3}(\frac{3}{5}){\displaystyle \frac{1}{2}}(x+1)=(\frac{3}{5})-3Asbasesaresamecomparethepowers\frac{1}{2}x+\frac{1}{2}=-3x+1=-6x=-7$

$$\begin{gathered} 2.{64}^{-\frac{1}{3}}({64}^{\frac{1}{3}}-{64}^{\frac{2}{3}}) \\ {4}^{3\left(\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\right)}(4^{3(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3)$}\right.}-4^{3(\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3)$}\right.}) \\ {4}^{-1}(4-4^2) \\ \frac{1}{4}(4-16)=-3 \end{gathered}$$