Question
Simplify:
$\frac{(25)^{\frac{3}{2}}\times(243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}}\times(8)^{\frac{4}{3}}}$
$\frac{(25)^{\frac{3}{2}}\times(243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}}\times(8)^{\frac{4}{3}}}$
✓
Answer
We have,
$\frac{(25)^{\frac{3}{2}}\times(243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}}\times(8)^{\frac{4}{3}}}=\frac{(5^2)^{\frac{3}{2}}\times(3^5)^{\frac{3}{5}}}{(2^4)^{\frac{5}{4}}\times(2^3)^{\frac{4}{3}}}$
$=\frac{5^{2\times\frac{3}{2}}\times3\times^{5\times\frac{3}{2}}}{2^{4\times\frac{5}{4}}\times2^{3\times\frac{4}{3}}}$
$=\frac{5^3\times3^3}{2^5\times2^4}$
$=\frac{125\times127}{32\times16}$
$=\frac{3375}{512}$
$\Rightarrow\frac{(25)^{\frac{3}{2}}(243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}}\times(8)^{\frac{4}{3}}}=\frac{3375}{512}$
$\frac{(25)^{\frac{3}{2}}\times(243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}}\times(8)^{\frac{4}{3}}}=\frac{(5^2)^{\frac{3}{2}}\times(3^5)^{\frac{3}{5}}}{(2^4)^{\frac{5}{4}}\times(2^3)^{\frac{4}{3}}}$
$=\frac{5^{2\times\frac{3}{2}}\times3\times^{5\times\frac{3}{2}}}{2^{4\times\frac{5}{4}}\times2^{3\times\frac{4}{3}}}$
$=\frac{5^3\times3^3}{2^5\times2^4}$
$=\frac{125\times127}{32\times16}$
$=\frac{3375}{512}$
$\Rightarrow\frac{(25)^{\frac{3}{2}}(243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}}\times(8)^{\frac{4}{3}}}=\frac{3375}{512}$
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
A heap of wheat is in the form of a cone of diameter 9m and height 3.5m. Find its volume. How much is canvas cloth required to just cover the heap? $($Use $\pi=3.14).$
→Define supplementary angles.
Find five rational numbers between $\frac{3}{5}$ and $\frac{2}{3}.$
→If $a - b = 6$ and $ab = 20,$ find the value of $a^3 - b^3.$
→If $a + b = 7$ and $ab = 12,$ find the value of $a^2 + b^2$
→If $3x - 2y = 11$ and $xy = 12,$ find the value of $27x^3 - 8y^3.$
→A cylindrical container with diameter of base 56cm contains sufficient water to submerge a rectangular solid of iron with dimensions (32cm × 22cm × 14cm). Find the rise in the level of water when the solid is completely submerged.
Find the median of:
$72, 63, 29, 51, 35, 60, 55, 91, 85, 82$
→$72, 63, 29, 51, 35, 60, 55, 91, 85, 82$
If $a + b = 8$ and $ab = 6,$ find the value of $a^3 + b^3.$
→If ABCD is a cyclic quadrilateral in which AD || BC. Prove that $\angle\text{B}=\angle\text{C}.$
→