Question

Exercises 177–179 will help you prepare for the material covered in the next section. If −8-8 is substituted for x in the equation 5x23+11x13+2=0 $$5x^{\frac{2}$${3}} + $$11x^{\frac{1}$${3}} + 2 = 0 , is the resulting statement true or false?

Accepted Answer

First, recognize that the equation given is $$5x^{\frac{2}$${3}} + $$11x^{\frac{1}$${3}} + 2 = 0$$. We need to substitute x = -8$ into this equation and check if the resulting statement is true or false. Next, calculate x$$^{\frac{1}$${3}}$$ when $$x = -8. $$Since the exponent $$\frac{1}{3}$$ represents the cube root, find $$\sqrt[3]{-8}. $$Then, use the value of $$x^{\frac{1}$${3}}$$ to find x$$^{\frac{2}$${3}}. $$Recall that $$x^{\frac{2}$${3}} = \$$left(x^{\frac{1}$${3}}\$$right)^2. $$Substitute the values of $$x^{\frac{2}$${3}}$$ and x$$^{\frac{1}$${3}}$$ back into the original equation: $$5x^{\frac{2}$${3}} + $$11x^{\frac{1}$${3}} + 2$$. Finally, simplify the expression step-by-step and determine if the result equals zero. If it does, the statement is true; if not, it is false.

Exercises 177–179 will help you prepare for the material covered in the next section. If $negative 8$ is substituted for x in the equation $5 x^{\frac{2}{3}} + 11 x^{\frac{1}{3}} + 2 = 0$ , is the resulting statement true or false?

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Key Concepts

Evaluating Expressions with Rational Exponents

Substitution in Algebraic Equations

Checking the Validity of an Equation

Exercises 177–179 will help you prepare for the material covered in the next section. If −8-8 is substituted for x in the equation 5x23+11x13+2=0 5x^{\(\frac{2}{3}\)} + 11x^{\(\frac{1}{3}\)} + 2 = 0 , is the resulting statement true or false?