Question

Which of the following expressions are equivalent? Justify your reasoning.
A) 4 square root of x^3
B) 1/x^-1
C) 10 square root x^5*x^4*x^2
D) x^1/3*x^1/3*x^1/3

Answer 1

Please someone help me figure this out

Answer 2

work out the powers inside the roots or reciprocals first.
Then a sqrt is just raising the number by power of half.
Negative powers on denominator become positive powers on the numerator and vice versa.

I can actually guess the answer by inspection just by looking at the coefficients of x
You should find B and D are the equivalent pair if you do what I've told you.

These rules will help
\[a^m \times a^n = a^{m+n} \]
\[a^{-1} = 1/a\] and \[\frac{ 1 }{ a^{-1} } = \frac{ 1 }{ \frac{ 1 }{ a } } = a\]
\[\sqrt{a} = a^{1/2} \]