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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

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

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

  • \[\frac{3}{10} \times \frac{3}{10} \times \frac{3}{10}\]

  • \[\sqrt{\frac{100}{9}} \times \sqrt{\frac{100}{9}} \times \sqrt{\frac{100}{9}}\]

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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?
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APPEARS IN

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