Kyran Hudson

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.

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$\left(\frac{2}{3}\right)\text{}\text{power because}\text{}{\displaystyle \left(\frac{2}{3}\right)\text{}\text{is reciprocal of}\text{}{\displaystyle \left(\frac{3}{2}\right):}}$

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

Simplify it further:

$x={\left({2}^{3}\right)}^{\frac{2}{3}}$

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

$x={\left(2\right)}^{2}$

$x=4$

Therefore,$x=4\text{}\text{is the}\text{}{\displaystyle \sqrt{}}$ of the equation.

Check:

Substitute$x=4$ into the original equation:

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

Simplify further:

${\left({2}^{2}\right)}^{\frac{3}{2}}=8$

${\left(2\right)}^{2\times \frac{3}{2}}=8$

${\left(2\right)}^{3}=8$

$8=8$

Thus, left-hand side is equal to the right-hand side of the original expression.

Conclusion:

Hence,$x=\left\{4\right\}\text{}\text{is the solution set of the equation}\text{}{\displaystyle {x}^{\frac{3}{2}}=8}$ and is verified.

The equation with rational exponents

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

Simplify it further:

Therefore,

Check:

Substitute

Simplify further:

Thus, left-hand side is equal to the right-hand side of the original expression.

Conclusion:

Hence,

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