Question

2.
Evaluate : (32)3
p.
8.0
(3)5 x​

Answer 1

Answer:

One of the laws of indices deals with cases where there are powers and roots at the same time.

x

p

q

=

q

√

x

p

=

(

q

√

x

)

p

The denominator shows the root and the numerator gives the power.

Note that the power can be inside or outside the root.

I prefer to find the root first, and then raise to the power because this keeps the numbers smaller. They can usually be calculated mentally rather than needing a calculator

32

2

5

=

(

5

√

32

)

2

=

2

2

w

w

w

w

w

w

w

w

w

w

w

w

w

(

2

⋅

2

⋅

2

⋅

2

⋅

2

=

2

5

=

32

)

=

4

Compare this with the other method of squaring first.

5

√

32

2

=

5

√

1024

=

4

While I know that

2

5

=

32

, the square of

32

and the fifth root of

1024

are not facts that I would be able to recall from memory.