Chapter ISG, Problem 7.3.1P

To determine

To choose the correct method

Answer to Problem 7.3.1P

Both method is incorrect.

Explanation of Solution

Given information:

Expression: ${27}^{\frac{2}{3}}$

Calculation:

Sa’s method,

Taking cubed root of 729,

= $\sqrt[3]{729}$

Solving,

= $\sqrt[3]{9\times 9\times 9}$

Now,

=9

Ma’s method

Squaring 3,

= ${(3)}^2$

Solving,

=9

Now, solving given expression,

= ${27}^{\frac{2}{3}}$

So,

= ${\left\{{(3)}^3\right\}}^{\frac{2}{3}}$

Using property,

= ${(3)}^{3\times \frac{2}{3}}$

And,

= ${(3)}^2$

Hence, solution of expression is 9.

This method is correct to evaluate. Hence, both method is incorrect.