anonymous
  • anonymous
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
Mathematics
jamiebookeater
  • jamiebookeater
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rhr12
  • rhr12
1/x^-1
rhr12
  • rhr12
Sorry
rhr12
  • rhr12
Last one

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anonymous
  • anonymous
@rhr12 what?
Jacob902
  • 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
rhr12
  • rhr12
last one is the answer
rhr12
  • rhr12
as i think
Jacob902
  • Jacob902
its c
Jacob902
  • Jacob902
no thinking
anonymous
  • anonymous
this is what they look like \[4\sqrt[]{x^3}\] \[\frac{ 1 }{ x^-1 }\] \[10\sqrt{x^5*x^4*x^2}\] \[x \frac{ 1 }{ 3 }*x \frac{ 1 }{ 3 }*x \frac{ 1 }{ 3 }\]
anonymous
  • anonymous
@Jacob902 so are none of them equivalent?
mathstudent55
  • 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: \(\large 4 \sqrt{x^3} =\color{red}{ 4|x|\sqrt {x}} \) \(\large \dfrac{1}{x^{-1}} = \dfrac{1}{\frac{1}{x}} = \color{red}{x} \) \(\large 10 \sqrt{x^5 \cdot x^4 \cdot x^2}= 10 \sqrt{x^{5 + 4 + 2}} = 10 \sqrt {x^{11}} = \color{red}{10 |x^5|\sqrt x}\) \(\large x^{-\frac{1}{3}} \times x^{-\frac{1}{3}} \times x^{-\frac{1}{3}} = x^{\frac{1}{3} + \frac{1}{3} + \frac{1}{3} } = x^1 = \color{red}{x}\)

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