Tips And Tricks And Shortcuts For Surds And Indices

Type 1: Surds and Indices -Simplify the expression

Question 1. Find the value (1728)^{( –  \frac{2}{3})}

Options.

A. \frac{1}{144}

B. 144

C. – \frac{1}{144}

D. \frac{1}{12}

Solution:     Cube root of 1728 is 12.

Therefore,(12)^{–3( \frac{1}{3})}

(12) ^{– 3 × ( \frac{2}{3})} = 12^–2

We know that, a^-n = ^{\frac{1}{a^n}}

Therefore, 12^–2 = (\frac{1}{12})^2 = \frac{1}{144}

Correct option: A

Type 2 : Surds and Indices- Find the value of x

Question 1. Find the value of x  If ( \frac{p}{q})^x-1 = ( \frac{q}{p})^x-3

Options.

A. 3

B. 2

C. 1

D. -2

Solution:    ( \frac{p}{q})^x-1 = ( \frac{q}{p})^x-3

( \frac{p}{q})^x-1 = ( \frac{p}{q})^-(x-3)

( \frac{p}{q})^x-1 = ( \frac{p}{q})^3-x

x-1 = 3-x

x = 2

Correct option: B