# Which One of the Following is Not Equal to ( 100 9 ) − 3 / 2 ? - Mathematics

MCQ

Which one of the following is not equal to $\left( \frac{100}{9} \right)^{- 3/2}$?

#### Options

• $\left( \frac{9}{100} \right)^{3/2}$

• $\left( \frac{1}{\frac{100}{9}} \right)^{3/2}$

• $\frac{3}{10} \times \frac{3}{10} \times \frac{3}{10}$

• $\sqrt{\frac{100}{9}} \times \sqrt{\frac{100}{9}} \times \sqrt{\frac{100}{9}}$

#### Solution

We have to find the value of ((100)/9)^(3/2)

So,

((100)/9)^(-3/2) = ((10^2)/3^2)^(-3/2

=(10^(2xx 3/2))/(3^(2xx 3/2))

= (10^(2xx 3/2))/(3^(2xx 3/2))

= 10^-3/3^-3

((100)/9)^(3/2) = (1/10^3)/(1/3^3)

=1/(10 xx 10 xx 10) xx (3xx3xx3)/1

= (3xx3xx3)/(10xx10xx10)

Since, (100/9)^(3/2) is equal to   (9/100)^(3/2),,  1/((100/9)^(3/2)) (3xx3xx3)/(10xx 10xx10).

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 2 Exponents of Real Numbers
Q 13 | Page 30