Question

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

a. 4√x3
b. 1/(x^-1)
c. 10√x5•x4•x2
d. x^1/3* x^1/3* x^1/3

Answer 1

Expressions a and d are equivalent.

Step-by-step explanation:

Let's go through each option to determine which expressions are equivalent.

a. 4√x³ = (4 * x^(1/3)) = (4 * (x^1/3))

b. 1/(x^-1) = x^1 = (1/x)

c. 10√x^5 • x^4 • x^2 = (10 * (x^(5/2)) * (x^4) * (x^2)) = 10x^(5/2 + 4 + 2) = 10x^(15/2)

d. x^(1/3) * x^(1/3) * x^(1/3) = ((x^1/3)^3) = x^1 = x

From the above calculations, we can see that expressions a and d are equivalent. Thus, the correct answer is: a and d.

Answer 2

`\boxed{b}\ and\ \boxed{d}\\\\b.\ (1)/(x^(-1))=\left((1)/(x)\right)^(-1)=x\\\\d.\ x^{(1)/(3)}\cdot x^{(1)/(3)}\cdot x^{(1)/(3)}=x^{(1)/(3)+(1)/(3)+(1)/(3)}=x^{(3)/(3)}=x^1=x`