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

Kyran Hudson 2020-11-10 Answered
The values of x that satisfy the equation with rational exponents x32=8 and check all the proposed solutions.
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Dora
Answered 2020-11-11 Author has 98 answers
Given:
The equation with rational exponents x32=8.
To isolate the variable, raise both sides of the equation to the (23) power because (23) is reciprocal of (32):
(x32)23=(8)23
Simplify it further:
x=(23)23
x=(2)3×23
x=(2)2
x=4
Therefore, x=4 is the  of the equation.
Check:
Substitute x=4 into the original equation:
(4)32=8
Simplify further:
(22)32=8
(2)2×32=8
(2)3=8
8=8
Thus, left-hand side is equal to the right-hand side of the original expression.
Conclusion:
Hence, x={4} is the solution set of the equation x32=8 and is verified.
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