800(0.1)^5/2(√2-1) how to solve
Answers
Step-by-step explanation:
The value of 800 × 0.1^\dfrac{5}{2}0.1
2
5
= \dfrac{800}{\sqrt{10} }
10
800
Step-by-step explanation:
We have,
800 × 0.1^\dfrac{5}{2}0.1
2
5
To find, the value of 800 × 0.1^\dfrac{5}{2}0.1
2
5
= ?
∴ 800 × 0.1^\dfrac{5}{2}0.1
2
5
= 800 × (\dfrac{1}{10} )^\dfrac{5}{2}(
10
1
)
2
5
Using the exponential identity,
(\dfrac{a}{b})^m=\dfrac{a^m}{b^m}(
b
a
)
m
=
b
m
a
m
= 800 × (\dfrac{1^{\dfrac{5}{2}}}{10^{\dfrac{5}{2}}} )(
10
2
5
1
2
5
)
= 800 × \dfrac{1}{100\times 10^\dfrac{1}{2}}}
= 800 × \dfrac{1}{10^{\dfrac{1}{2} }}
10
2
1
1
= \dfrac{800}{\sqrt{10} }
10
800
∴ The value of 800 × 0.1^\dfrac{5}{2}0.1
2
5
= \dfrac{800}{\sqrt{10} }
10
800
Thus, the value of 800 × 0.1^\dfrac{5}{2}0.1
2
5
is equal to \dfrac{800}{\sqrt{10} }
10
800
,