The values of x that satisfy the equation with rational exponents x32=8 and check all the proposed solutions.

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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College
Calculus and Analysis
Integral Calculus
Rational exponents and radicals

Kyran Hudson

Answered question

2020-11-10

The values of x that satisfy the equation with rational exponents

x^{\frac{3}{2}} = 8

and check all the proposed solutions.

Answer & Explanation

Dora

Skilled2020-11-11Added 98 answers

Given:
The equation with rational exponents

x^{\frac{3}{2}} = 8 .

To isolate the variable, raise both sides of the equation to the

(\frac{2}{3}) power because (\frac{2}{3}) is reciprocal of (\frac{3}{2}) :

{(x^{\frac{3}{2}})}^{\frac{2}{3}} = {(8)}^{\frac{2}{3}}

Simplify it further:

x = {(2^{3})}^{\frac{2}{3}}

x = {(2)}^{3 \times \frac{2}{3}}

x = {(2)}^{2}

x = 4

Therefore,

x = 4 is the \sqrt{}

of the equation.
Check:
Substitute

x = 4

into the original equation:

{(4)}^{\frac{3}{2}} = 8

Simplify further:

{(2^{2})}^{\frac{3}{2}} = 8

{(2)}^{2 \times \frac{3}{2}} = 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 x^{\frac{3}{2}} = 8

and is verified.

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