When a power is raised to another , the powers can be combined into one by multiplying them. For example
(52)3 can be rewritten with this rule as follows.
(52)3⇒52⋅3=56
This rule can be explained by writing the powers as products.
(52)3 a3=a⋅a⋅a 52⋅52⋅52 5⋅5⋅5⋅5⋅5⋅5
This rule is valid for all values of
m and
n when
a=0. For the rule to be true also for
a=0 it is necessary that both exponents are greater than
0. Note that the rule might lead to non-real solutions when
a<0 and at least one of the exponents is not an integer.