## anonymous one year ago Which of the following expressions are equivalent? Justify your reasoning. 4√x3 1/x^-1 10√x5•x4•x2 x*^1/3x*^1/3x*^1/3

1. rhr12

1/x^-1

2. rhr12

Sorry

3. rhr12

Last one

4. anonymous

@rhr12 what?

5. Jacob902

You are using some wobbly notation. If I read it correctly, the second and fourth are close, but not actually equivalent. 1/x⁻¹ = x, for x ≠ 0 x^(1/3) · x^(1/3) · x^(1/3) = x^(1/3 + 1/3 + 1/3) = x¹ = x

6. rhr12

7. rhr12

as i think

8. Jacob902

its c

9. Jacob902

no thinking

10. anonymous

this is what they look like $4\sqrt[]{x^3}$ $\frac{ 1 }{ x^-1 }$ $10\sqrt{x^5*x^4*x^2}$ $x \frac{ 1 }{ 3 }*x \frac{ 1 }{ 3 }*x \frac{ 1 }{ 3 }$

11. anonymous

@Jacob902 so are none of them equivalent?

12. mathstudent55

$$\large 4 \sqrt{x^3}$$ $$\large \dfrac{1}{x^{-1}}$$ $$\large 10 \sqrt{x^5 \cdot x^4 \cdot x^2}$$ $$\large x^{-\frac{1}{3}} \times x^{-\frac{1}{3}} \times x^{-\frac{1}{3}}$$ Solutions: $$\large 4 \sqrt{x^3} =\color{red}{ 4|x|\sqrt {x}}$$ $$\large \dfrac{1}{x^{-1}} = \dfrac{1}{\frac{1}{x}} = \color{red}{x}$$ $$\large 10 \sqrt{x^5 \cdot x^4 \cdot x^2}= 10 \sqrt{x^{5 + 4 + 2}} = 10 \sqrt {x^{11}} = \color{red}{10 |x^5|\sqrt x}$$ $$\large x^{-\frac{1}{3}} \times x^{-\frac{1}{3}} \times x^{-\frac{1}{3}} = x^{\frac{1}{3} + \frac{1}{3} + \frac{1}{3} } = x^1 = \color{red}{x}$$