Question

find the value of =(32)0.2+(81)0.25/(256)0.5-(121)0.5​

Answer 1

Answer:

[32(0.2)+81(0.25)]/[256(0.5)-121(0.5)]=0.3948148148

Answer 2

Answer:

$\frac{(32)^{0.2}+(81)^{0.25}}{(256)^{0.5}-(121)^{0.5}}=1$

Step-by-step explanation:

Given : Expression $\frac{(32)^{0.2}+(81)^{0.25}}{(256)^{0.5}-(121)^{0.5}}$

To find : The value of the expression ?

Solution :

Step 1 - Write the expression,

$\frac{(32)^{0.2}+(81)^{0.25}}{(256)^{0.5}-(121)^{0.5}}$

Step 2 - Remove decimal in powers,

$=\frac{(32)^{\frac{2}{10}}+(81)^{\frac{25}{100}}}{(256)^{\frac{5}{10}}-(121)^{\frac{5}{10}}}$

$=\frac{(32)^{\frac{1}{5}}+(81)^{\frac{1}{4}}}{(256)^{\frac{1}{2}}-(121)^{\frac{1}{2}}}$

Step 3 - Write number into their powers,

$=\frac{(2^5)^{\frac{1}{5}}+(3^4)^{\frac{1}{4}}}{(16^2)^{\frac{1}{2}}-(11^2)^{\frac{1}{2}}}$

$=\frac{2+3}{16-11}$

$=\frac{5}{5}$

$=1$

Therefore, $\frac{(32)^{0.2}+(81)^{0.25}}{(256)^{0.5}-(121)^{0.5}}=1$