The values of x that satisfy the equation with rational exponents (x+5)32=8 and check all the proposed solutions.

To isolate the variable, raise both sides of the equation to the (23) power because (23) is the reciprocal of (32): ((x+5)23)23=(8)23 Simplify it further: x+5=(23)23 x+5=(2)3⋅23 x+5=(2)2 x+5=4 Subtract 5 from both sides of the equation: x+5−5=4−5 Simplify further: x= −1 Therefore, x= −1 is the of the equation. Check: Subtitute x= −1 into the original equation: ((−1+5))32=8. Simplify further: (4)32=8 (22)32=8 (2)3=8 8=8 Thus, the left-hand side is equal to the right-hand side of the original expression. Conclusion: Hence, x={−1} is the solution set of the equation (x+5)32=8 is verified

Expert answers to "The values of x that satisfy the equation..."

College
Calculus and Analysis
Integral Calculus
Rational exponents and radicals

sjeikdom0

Answered question

2020-11-08

The values of x that satisfy the equation with rational exponents

{(x + 5)}^{\frac{3}{2}} = 8

and check all the proposed solutions.

Answer & Explanation

unett

Skilled2020-11-09Added 119 answers

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

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

{({(x + 5)}^{\frac{2}{3}})}^{\frac{2}{3}} = {(8)}^{\frac{2}{3}}

Simplify it further:

x + 5 = {(2^{3})}^{\frac{2}{3}}

x + 5 = {(2)}^{3 \cdot \frac{2}{3}}

x + 5 = {(2)}^{2}

x + 5 = 4

Subtract 5 from both sides of the equation:

x + 5 - 5 = 4 - 5

Simplify further:

x = - 1

Therefore,

x = - 1 is the \sqrt{}

of the equation.
Check:
Subtitute

x = - 1

into the original equation:

{((- 1 + 5))}^{\frac{3}{2}} = 8 .

Simplify further:

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

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

{(2)}^{3} = 8

8 = 8

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

x = {- 1} is the solution set of the equation {(x + 5)}^{\frac{3}{2}} = 8

is verified

Jeffrey Jordon

Expert2021-10-25Added 2605 answers

Answer is given below (on video)

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