# The values of x that satisfy the equation with rational exponents displaystyle{x}^{{frac{3}{{2}}}}={8} and check all the proposed solutions.

The values of x that satisfy the equation with rational exponents ${x}^{\frac{3}{2}}=8$ and check all the proposed solutions.
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Given:
The equation with rational exponents ${x}^{\frac{3}{2}}=8.$
To isolate the variable, raise both sides of the equation to the
${\left({x}^{\frac{3}{2}}\right)}^{\frac{2}{3}}={\left(8\right)}^{\frac{2}{3}}$
Simplify it further:
$x={\left({2}^{3}\right)}^{\frac{2}{3}}$
$x={\left(2\right)}^{3×\frac{2}{3}}$
$x={\left(2\right)}^{2}$
$x=4$
Therefore, of the equation.
Check:
Substitute $x=4$ into the original equation:
${\left(4\right)}^{\frac{3}{2}}=8$
Simplify further:
${\left({2}^{2}\right)}^{\frac{3}{2}}=8$
${\left(2\right)}^{2×\frac{3}{2}}=8$
${\left(2\right)}^{3}=8$
$8=8$
Thus, left-hand side is equal to the right-hand side of the original expression.
Conclusion:
Hence, and is verified.