Simplify 32to the power of 5
Answers
Answer:
1024
Step-by-step explanation:
There is a choice of methods.. Work smarter, not harder!
Explanation:
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.