2. Eg. The 2 and the a BOTH need to raised to 2.
The Power outside the brackets needs to be applied to all Bases
Inside the brackets. (Like the Distributive Law, but for Exponents).
(2a)
2
= 22
x a2
= 4 x a2
= 4a2
3. Eg. The a and the b BOTH need to be cubed.
2 3
2 x 2 x 2 23
3 3 x 3 x 3 33==
a 3
a x a x a a3
b b x b x b b3==
4. Eg. The a and the b BOTH need to be Powered.
The Expanding Quotients Rule involves
applying the Power Outside of the
brackets, onto every item that is inside
the brackets.
5. 5 4
5 4
54
3 3 34
Simplify the expression (5 / 3)4
We apply the Outside Power to both items:
==
6. m 6
m 6
m6
k k k6
Simplify the expression (m / k)6
We apply the Outside Power to both items:
==
8. ab2 3
ab2 3
a3
b2x3
a3
b6
c c c3
c3
Simplify the expression ( ab2
/ c ) 3
We apply the Outside Power to three items:
== =
For the ab2
, the a & b2
BOTH need to be Cubed.
9. Eg. Different Top and Bottom, but same Powers.
The Expanding Quotients Rule can also
be used in reverse, to make a fraction
with IDENTICAL POWERS into a
single bracketed exponent Fraction.
10. For Expanding Quotients Rule BACKWARDS, we have two different
bases, BUT THEY MUST BOTH BE RAISED TO THE SAME POWER.
62
62
6 2
22
22
2
= = = (3)2
or 9
h3
h3
h 3
h 3
43
43
4 4
= = =
a7
a7
a 7
a 7
c7
c7
c c
= = =
