How do you simplify (723)52?

1 Answer
Apr 15, 2018

(73)5

Explanation:

First, let's set out the exponent rules that are relevant:

(1) (ab)c=abc

(2) (ef)g=egfg

(3) (1h)j=hj

Now we first use rule (2):

(723)52=(72)52(13)52

We can now use rule (3):

(72)52(13)52=(72)52352

We use rule (1) to multiply out the left hand term:

(72)52352=7252352

=75352

To simplify further we could again use rule (1) and rule (3):

75352=(7312)5

As x12x

(7312)5=(73)5