How to solve these algebraically?

Hello Guest!

a)

\(\color{BrickRed}-2+5z^{-\frac{3}{2}}=133\\ 5z^{-\frac{3}{2}}=135\\ z^{-\frac{3}{2}}=27\\ z^{-3}=27^2\\ z^3=\frac{1}{27^2}\\ z=\frac{1}{\sqrt[3]{(3^3)^2}}\)

\(z=\frac{1}{9}\)

!

b)

\(\color{BrickRed}2,1x^{0,25}+5=7\\ x^{\frac{1}{4}}=\frac{2}{2,1}\\ x=(\frac{2}{2,1})^4 \)

\(x=(\frac{20}{21})^4=(\frac{2^2\cdot 5}{3\cdot 7})^4\)

\(x=\frac{2^8\cdot 5^4}{3^4\cdot7^4}=0,8227...\)

thank you so much !! very clear and was able to follow the steps :)

thank u so much !!