Express each of the following as radicals (25)¾
Answers
Answer:
GIVEN :
The expression is (\frac{13}{21})^{\frac{2}{5}}(
21
13
)
5
2
TO FIND :
The given expression in the radical form
SOLUTION :
Given expression is (\frac{13}{21})^{\frac{2}{5}}(
21
13
)
5
2
To express the given expression as a radical:
(\frac{13}{21})^{\frac{2}{5}}(
21
13
)
5
2
By using the formula in fractional exponent :
(\frac{a}{b})^m=\frac{a^m}{b^m}(
b
a
)
m
=
b
m
a
m
=\frac{(13)^{\frac{2}{5}}}{(21)^{\frac{2}{5}}}=
(21)
5
2
(13)
5
2
=\frac{(13)^{2.(\frac{1}{5})}}{(21)^{2.(\frac{1}{5})}}=
(21)
2.(
5
1
)
(13)
2.(
5
1
)
By using the formula in fractional exponent :
a^{mn}=(a^m)^na
mn
=(a
m
)
n
=\frac{(13^2)^{\frac{1}{5}}}{(21^2)^{\frac{1}{5}}}=
(21
2
)
5
1
(13
2
)
5
1
=\frac{(169)^{\frac{1}{5}}}{(441)^{\frac{1}{5}}}=
(441)
5
1
(169)
5
1
=\frac{\sqrt[5]{169}}{\sqrt[5]{441}}=
5
441
5
169
By using the square root of division property:
For b\neq 0b≠0 \frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}
n
b
n
a
=
n
b
a
=\sqrt[5]{\frac{169}{441}}=
5
441
169
∴ (\frac{13}{21})^{\frac{2}{5}}=\sqrt[5]{\frac{169}{441}}(
21
13
)
5
2
=
5
441
169
∴ the given expression (\frac{13}{21})^{\frac{2}{5}}(
21
13
)
5
2
as a radical form is \sqrt[5]{\frac{169}{441}}
5
441
169
Answer:
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