Question

Question 1Is the expression x^3*x^3*x^3equivalent to x^(3*3*3)? Why or why not? Explain your reasoning.No because the law of exponentsQuestion 2Rewrite in simplest radical form1/x^((-3)/6)Show each step of your process.Question 3Rewrite in simplest rational exponent form √x • 4√x. Show each step of your process.Question 4Rewrite in simplest radical formx^(5/6)/x^(1/6)Show each step of your process.Question 5Which of the following expressions are equivalent? Justify your reasoning.4√x31/x^(-1)10√x5•x4•x2x^(1/3)*x^(1/3)*x^(1/3)

Answer 1

Answer: Question 1) No, because according to the law of exponents

x³.x³.x³ = x³⁺³⁺³ = x⁹

and x⁽³*³*³⁾ = x²⁷

Question 2) √x

Question 3) 4x

Question 4) ∛x²

Question 5) B = D

Explanation:

Question 1) Is the expression x^3*x^3*x^3 equivalent to x^(3*3*3)? Why or why not? Explain your reasoning.

No, because according to the law of exponents

x³.x³.x³ = x³⁺³⁺³ = x⁹

and x⁽³*³*³⁾ = x²⁷

Question 2) Rewrite in simplest radical form 1/x^((-3)/6). Show each step of your process.

simplifying the denominator expoent: 1/x^((-3)/6) = 1/x^(-1/2)

apply the expoent to the hole fraction: 1/x^(-1/2) = (1/x)^(-1/2)

changing the signal on the expoent: (1/x)^(-1/2) = (x)^(1/2)

changing the expoent into root: (x)^(1/2) = √x

1/x^((-3)/6) = 1/x^(-1/2) = (1/x)^(-1/2) = (x)^(1/2) = √x

Question 3) Rewrite in simplest rational exponent form √x • 4√x. Show each step of your process.

√x • 4√x = 4√x • √x = 4√x² = 4x

Question 4) Rewrite in simplest radical formx^(5/6)/x^(1/6). Show each step of your process.

x^⁽⁵/⁶⁾/x^⁽¹/₆⁾ = x^⁽⁵/⁶⁾ • 1/x^⁽¹/₆⁾ = x^⁽⁵/⁶⁾ • x^⁽⁻¹/₆⁾ = x^⁽⁵/⁶ ⁻ ¹/⁶) = x^⁽⁴/⁶⁾ = x^⁽²/₃⁾ = ∛x²

Question 5) Which of the following expressions are equivalent? Justify your reasoning.

A. ⁴√x³ B. 1/x⁻¹ C. ¹⁰√x⁵•x⁴•x² D. x¹/³•x¹/³•x¹/³

A. ⁴√x³ = x³/⁴

B. 1/x⁻¹ = (1/x)⁻¹ = x

C. ¹⁰√x⁵•x⁴•x² = ¹⁰√x¹¹ = x¹¹/¹⁰

D. x¹/³•x¹/³•x¹/³ = x⁽¹/³⁺¹/³⁺¹/³⁾ = x³/³ = x

So, B = D