(32) (81) (256) (121)
Answers
Answer:
Answer:
\frac{(32)^{0.2}+(81)^{0.25}}{(256)^{0.5}-(121)^{0.5}}=1
(256)
0.5
−(121)
0.5
(32)
0.2
+(81)
0.25
=1
Step-by-step explanation:
Given : Expression \frac{(32)^{0.2}+(81)^{0.25}}{(256)^{0.5}-(121)^{0.5}}
(256)
0.5
−(121)
0.5
(32)
0.2
+(81)
0.25
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}}
(256)
0.5
−(121)
0.5
(32)
0.2
+(81)
0.25
Step 2 - Remove decimal in powers,
=\frac{(32)^{\frac{2}{10}}+(81)^{\frac{25}{100}}}{(256)^{\frac{5}{10}}-(121)^{\frac{5}{10}}}=
(256)
10
5
−(121)
10
5
(32)
10
2
+(81)
100
25
=\frac{(32)^{\frac{1}{5}}+(81)^{\frac{1}{4}}}{(256)^{\frac{1}{2}}-(121)^{\frac{1}{2}}}=
(256)
2
1
−(121)
2
1
(32)
5
1
+(81)
4
1
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}}}=
(16
2
)
2
1
−(11
2
)
2
1
(2
5
)
5
1
+(3
4
)
4
1
=\frac{2+3}{16-11}=
16−11
2+3
=\frac{5}{5}=
5
5
=1=1
Therefore, \frac{(32)^{0.2}+(81)^{0.25}}{(256)^{0.5}-(121)^{0.5}}=1
(256)
0.5
−(121)
0.5
(32)
0.2
+(81)
0.25
=1