Question

I need help and explanations with these 5 questions.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.a. 4√x3b. 1/x^(-1)c. 10√x5•x4•x2d. x^(1/3)*x^(1/3)*x^(1/3)

Answer 1

1) No. 2)
`√(x)` 3)4x 4)
`x^{(3)/(2)}` or
`√(x^3)`5) B and D.

Explanation:

Check the pictures below

1)
`x^(3) *x^(3)*x^(3)=x^(3+3+3)=x^(9)`x^(3*3*3)=x^{27}[/tex]

For the first, we must just repeat the base e sum the exponents

For the second one, we must multiply the exponents.

According to the Exponents Law.

`x^(m)*x^(n) =x^(m+n)\\x^(m*n) =x^(mn)`

2)

Here we have three combined Exponent laws, namely:

3)

First on multiplying keep the 4 outside the square root,

4) The starting point of it is reminding that in a fraction, whenever we divide two fractions we have to operate the product of the first fraction times the inverse of the second one.

Then we apply the Exponent Law of a divison between same base powers, repeating the base subtracting the exponents, and simplifying it:

`x^{(4)/(6)}=x^{(3)/(2)}`

5)

Check below

b and d, are equivalent between themselves since the same quantities of x are displayed. Notice, all we have used. Exponent Laws and Power Properties