The value of x is [tex]5\sqrt[3]{25}[/tex].
Solution:
Given expression is [tex]-7=8-3 \sqrt[5]{x^{3}}[/tex].
Switch both sides.
[tex]8-3 \sqrt[5]{x^{3}}=-7[/tex]
Subtract 8 from both side of the equation.
[tex]8-3 \sqrt[5]{x^{3}}-8=-7-8[/tex]
[tex]-3 \sqrt[5]{x^{3}}=-15[/tex]
Divide by –3 on both side of the equation.
[tex]$\frac{-3 \sqrt[5]{x^{3}}}{-3} =\frac{-15}{-3}[/tex]
[tex]\sqrt[5]{x^{3}}=-5[/tex]
To cancel the cube root, raise the power 5 on both sides.
[tex](\sqrt[5]{x^{3}})^5=(-5)^5[/tex]
[tex]x^3=3125[/tex]
To find the value of x, take square root on both sides.
[tex]\sqrt[3]{x^3}=\sqrt[3]{25}[/tex]
[tex]x=5\sqrt[3]{25}[/tex]
Hence the value of x is [tex]5\sqrt[3]{25}[/tex].
