Question
Simplify: $\Big(\frac{\sqrt{2}}{5}\Big)^8\div\Big(\frac{\sqrt{2}}{5}\Big)^{13}$
✓
Answer
We have, $\Big(\frac{\sqrt{2}}{5}\Big)^8\div\Big(\frac{\sqrt{2}}{5}\Big)^{13}$
$=\Big(\frac{\sqrt{2}}{5}\Big)^8\times\Big(\frac{5}{\sqrt{2}}\Big)^{13}$
$=\frac{(\sqrt{2})^8}{5^8}\times\frac{5^{13}}{(\sqrt{2})^{13}}$
$=\frac{5^{13}\times5^{-8}}{(\sqrt{2})^{13}\times(\sqrt{2})^{-8}}$
$=\frac{5^{13-8}}{(\sqrt{2})^{13-8}}$
$=\frac{5^5}{(\sqrt{2})^5}=\frac{3125}{4\sqrt{2}}$
$\Rightarrow\Big(\frac{\sqrt{2}}{5}\Big)\div\Big(\frac{\sqrt{2}}{5}\Big)^{13}=\frac{3125}{4\sqrt{2}}$
$=\Big(\frac{\sqrt{2}}{5}\Big)^8\times\Big(\frac{5}{\sqrt{2}}\Big)^{13}$
$=\frac{(\sqrt{2})^8}{5^8}\times\frac{5^{13}}{(\sqrt{2})^{13}}$
$=\frac{5^{13}\times5^{-8}}{(\sqrt{2})^{13}\times(\sqrt{2})^{-8}}$
$=\frac{5^{13-8}}{(\sqrt{2})^{13-8}}$
$=\frac{5^5}{(\sqrt{2})^5}=\frac{3125}{4\sqrt{2}}$
$\Rightarrow\Big(\frac{\sqrt{2}}{5}\Big)\div\Big(\frac{\sqrt{2}}{5}\Big)^{13}=\frac{3125}{4\sqrt{2}}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Simplify: $\frac{(25)^{\frac{3}{2}}\times(243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}}\times(8)^{\frac{4}{3}}}$
→In figure, $\text{ABCD}$ and $\text{PQRC}$ are rectangles and $Q$ is the mid$-$point of $AC$. Prove that
$i. DP = PC$
$ii. \text{PR}=\Big(\frac{1}{2}\Big)\text{AC}$
→$i. DP = PC$
$ii. \text{PR}=\Big(\frac{1}{2}\Big)\text{AC}$
Prove that: $\Big(\frac{\text{x}^\text{a}}{\text{x}^\text{b}}\Big)^{\text{a}^2+\text{ab}+\text{b}^2}\times\Big(\frac{\text{x}^2}{\text{x}^\text{c}}\Big)^{\text{b}^2+\text{bc}+\text{c}^2}\times\Big(\frac{\text{x}^\text{c}}{\text{x}^\text{a}}\Big)^{\text{c}^2+\text{ca}+\text{a}^2}=1$
→Find the irrational number between $\frac{1}{7}$and $\frac{2}{7}.$
→A triangular park $ABC$ has sides $120 m, 80 m$ and $50 \ m$ . (in a given figure). A gardener Dhania has to put a fence all around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of ₹ $20$ per metre leaving a space $3$ m wide for a gate on one side.
→The follwoing data give the number of boys of a particular age in a class of $40 $students.
Calculate the mean age of the students.
→|
Age (in years)
|
$15$
|
$16$
|
$17$
|
$18$
|
$19$
|
$20$
|
|
Frequency ($f_i$)
|
$3$
|
$8$
|
$9$
|
$11$
|
$6$
|
$3$
|
If $P$ is any point in the interior of a parallelogram $ABCD$, then prove that area of the triangle $APB$ is less than half the area of parallelogram.
→Evaluate the following:
$104^3+96^3$
→$104^3+96^3$
Show that the angles of an equilateral triangle are $60^\circ $ each.
→The following table shows the number of scooters sold by a dealer during six consecutive years. Draw a bar graph to represent this data.
→|
Year
|
$2011$
|
$2012$
|
$2013$
|
$2014$
|
$2015$
|
$2016$
|
|
Number of scooters sold (in thousands)
|
$16$
|
$20$
|
$32$
|
$36$
|
$40$
|
$48$
|