Question

Select all radical expressions that are equivalent to 41 3/5

Answer 1

Answer:

x^ \frac{m}{n} = \sqrt[n]{x^m}x

n

m

=

n

x

m

and

(x^m)^n=x^{mn}(x

m

)

n

=x

mn

so

x^ \frac{3}{5} = \sqrt[5]{4^3}x

5

3

=

5

4

3

but wait, there's more

4=2², so

x^ \frac{3}{5} = \sqrt[5]{4^3} = \sqrt[5]{(2^2)^3} = \sqrt[5]{2^6}x

5

3

=

5

4

3

=

5

(2

2

)

3

=

5

2

6

=

2^ \frac{6}{5}=(2^ \frac{5}{5})(2^ \frac{1}{5})=2 \sqrt[5]{2}2

5

6

=(2

5

5

)(2

5

1

)=2

5

2

also, 4^3=64