Question

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

Answer 1

1/x^-1

Answer 2

Sorry

Answer 3

Last one

Answer 4

@rhr12 what?

Answer 5

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

Answer 6

last one is the answer

Answer 7

as i think

Answer 8

its c

Answer 9

no thinking

Answer 10

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

Answer 11

@Jacob902 so are none of them equivalent?

Answer 12

\(\large 4 \sqrt{x^3} \)

\(\large \dfrac{1}{x^{-1}} \)

\(\large 10 \sqrt{x^5 \cdot x^4 \cdot x^2}\)

\(\large x^{-\frac{1}{3}} \times x^{-\frac{1}{3}} \times x^{-\frac{1}{3}}\)

Solutions:

\(\large 4 \sqrt{x^3} =\color{red}{ 4|x|\sqrt {x}} \)

\(\large \dfrac{1}{x^{-1}} = \dfrac{1}{\frac{1}{x}} = \color{red}{x} \)

\(\large 10 \sqrt{x^5 \cdot x^4 \cdot x^2}= 10 \sqrt{x^{5 + 4 + 2}} = 10 \sqrt {x^{11}} = \color{red}{10 |x^5|\sqrt x}\)

\(\large x^{-\frac{1}{3}} \times x^{-\frac{1}{3}} \times x^{-\frac{1}{3}}
= x^{\frac{1}{3} + \frac{1}{3} + \frac{1}{3} } = x^1 = \color{red}{x}\)