Question
Evaluate :$\left(\frac{27}{8}\right)^{\frac{2}{3}}-\left(\frac{1}{4}\right)^{-2}+5^0$
✓
Answer
$ \left(\frac{27}{8}\right)^{\frac{2}{3}}-\left(\frac{1}{4}\right)^{-2}+5^0$
$ =\left(\frac{3 \times 3 \times 3}{2 \times 2 \times 2}\right)^{\frac{2}{3}}-\left(\frac{1 \times 1}{2 \times 2}\right)^{-2}+5^0$
$ =\left[\left(\frac{3}{2}\right)^3\right]^{\frac{2}{3}}-\left[\left(\frac{1}{2}\right)^2\right]^{-2}+1$
$ =\left(\frac{3}{2}\right)^{3 \times \frac{2}{3}}-\left(\frac{1}{2}\right)^{2 \times(-2)}+1$
$ =\left(\frac{3}{2}\right)^2-\left(\frac{1}{2}\right)^{-4}+1$
$ =\frac{3}{2} \times \frac{3}{2}-\frac{1}{\left(\frac{1}{2}\right)^4}+1$
$ =\frac{9}{4}-\frac{1}{\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}}+1$
$ =\frac{9}{4}-\frac{1}{\frac{1}{16}}+1$
$ =\frac{9}{4}-16+1$
$ =\frac{9-64+4}{4}$
$ =\frac{-51}{4}$
$ =\left(\frac{3 \times 3 \times 3}{2 \times 2 \times 2}\right)^{\frac{2}{3}}-\left(\frac{1 \times 1}{2 \times 2}\right)^{-2}+5^0$
$ =\left[\left(\frac{3}{2}\right)^3\right]^{\frac{2}{3}}-\left[\left(\frac{1}{2}\right)^2\right]^{-2}+1$
$ =\left(\frac{3}{2}\right)^{3 \times \frac{2}{3}}-\left(\frac{1}{2}\right)^{2 \times(-2)}+1$
$ =\left(\frac{3}{2}\right)^2-\left(\frac{1}{2}\right)^{-4}+1$
$ =\frac{3}{2} \times \frac{3}{2}-\frac{1}{\left(\frac{1}{2}\right)^4}+1$
$ =\frac{9}{4}-\frac{1}{\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}}+1$
$ =\frac{9}{4}-\frac{1}{\frac{1}{16}}+1$
$ =\frac{9}{4}-16+1$
$ =\frac{9-64+4}{4}$
$ =\frac{-51}{4}$
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
If $\frac{9^n \times 3^2 \times 3^n-(27)^n}{3^{3 m} \times 2^3}=3^{-3}$, prove that $(m-n)=1$.
→The following figure shows a circle with center $O$.
If $O P$ is perpendicular to $A B$, prove that $A P=B P$.
→If $O P$ is perpendicular to $A B$, prove that $A P=B P$.
A boy played $100$ games, gaining $Rs. 50 $ on each game that he won, and losing $Rs. 20$ for each game that he lost. If on the whole he gained $Rs. 800$, find the number of games that he won.
→Find the shaded area in the given figure.
A ladder $25\ m$ long reaches a window of a building $20\ m$ above the ground. Determine the distance of the foot of the ladder from the building.
→Construct a rhombus, having given one side $= 4.8 \ cm$ and one angle $= 75^o.$
→The perimeter of a square plot of land is $64\ m$. The area of a nearby rectangular plot is $24\ m^2$ more than the area of the given square. If the length of the rectangle is $14\ m$, find its breadth.
→In the given figure, $\angle PSR =90, PQ =10 cm$, $QS =6 cm$ and $RQ =9 cm$, calculate the length of PR.
→Solve the following systems of equation by using the method of cross multiplication:
$5 x-4 y+2=0,2 x+3 y=13$
→$5 x-4 y+2=0,2 x+3 y=13$
Draw the graph of the equation $2x - 3y - 5 = 0$From the graph, find :$(i) \ x_1,$ the value of $x,$ when $y = 7;(ii) \ x_2,$ the value of $x,$ when $y = - 5.$
→