Download App

Exponents Of Real Numbers [NEW] — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsExponents Of Real Numbers [NEW]1 Mark
MCQ
Which of the following is the greatest?
  • A
    $7^2$
  • ✓
    $(49)^{3 / 2}$
  • C
    $\left(\frac{1}{343}\right)^{-1 / 3}$
  • D
    $(2401)^{-1 / 4}$
✓

Answer

Correct option: B.
$(49)^{3 / 2}$
(b)
We find that
$(49)^{3 / 2}=\left(7^2\right)^{3 / 2}=7^{2 \times 3 / 2}=7^3$$ \left(\frac{1}{343}\right)^{-1 / 3}=\left(\frac{1}{7^3}\right)^{-1 / 3}=\left(7^{-3}\right)^{-1 / 3}=7^{-3 \times-\frac{1}{3}}=7 $
and $(2401)^{-1 / 4}=\left(7^4\right)^{-1 / 4}=7^{4 \times-\frac{1}{4}}=7^{-1}=\frac{1}{7}$
Clearly, $\frac{1}{7}<7<7^2<7^3 \Rightarrow(2401)^{-1 / 4}<\left(\frac{1}{343}\right)^{-1 / 3}<7^2<(49)^{3 / 2}$ [Using (i), (ii) and (iii)]
Hence, $(49)^{3 / 2}$ is the greatest..

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q" from Exponents Of Real Numbers [NEW]→Exponents Of Real Numbers [NEW] — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

For a given data, the difference between the maximum and minimum observation is known as its.
→
The figure formed by joining the mid-points of the adjacent sides of a parallelogram is a:
→
If the height of a cylinder is doubled and radius remains the same, then volume will be:
  1. Doubled.
  2. Halved.
  3. Same.
  4. Four times.
→
A cube whose volume is $\frac{1}{8}$ cubic centimeter is placed on top of a cube whose volume is 1cm3. The two cubes are then placed on top of a third cube whose volume is 8cm3. The height of the stacked cubes is:
→
If $x-3$ is a factor of $x^2-a x-15$, then $a=$
→
In $\angle\text{ABC}$ and $\angle\text{DEF},$ AB = DE and $\angle\text{A} = \angle\text{D}.$ Then, the two triangles will be congruent by SAS axiom if:
→
In the given figure, O is the centre of a circle and $\angle\text{AOB}=140^\circ.$ Then, $\angle\text{ACB}=?$
→
A rational number lying between $\sqrt{2}$ and $\sqrt{3}$ is:
→
If $x+y=12$ and $x y=27$, then $x^3+y^3=$
→
The representation of $1 . \overline{3}$ in the form p/q is
→