Question

Tyrone claims that the first step to simplfy this expression is to raise the numerator and denominator to the third power. Alisha claims that the first step to simplfy is to apply the qoutient of powers. Who is correct? Explain.

Answer 1

Alisha's approach is simpler and less complicated

Explanation:

Given:

(m^2*n^-3) / (m^6*n^-1)

Tyrone's approach.

(m^2*n^-3) / (m^6*n^-1)

(m^2*n^-3)^3 / (m^6*n^-1)^3

You can find the cube root of both the numerator and denominator in order to eliminate the third power

3√((m^2*n^-3)^3 / 3√(m^6*n^-1)^3

This will take us back to the original expression

(m^2*n^-3) / (m^6*n^-1)

= m^(2-6)*n^(-3+1)

= m^-4*n^-2

= 1/(m^4*n^2)

Alisha's approach.

(m^2*n^-3)/(m^6*n^-1)

= m^(2-6)*n^(-3+1)

= m^-4*n^-2

= 1/(m^4*n^2)

The approach of both of them are correct, however, Tyrone's approach will make the expression more complicated but they would still arrive at the same answer. 1/(m^4*n^2)