Express using positive exponents

K

karipeters

New member
Joined
Dec 5, 2011
Messages
13
Express using positive exponents, simplify if possible.

(A over 2)^-4.

I haven't the slightest idea what I am doing here and the textbook did a poor job of explaining how to do this. Can someone please show me step by step what I am suppose to do to solve this?
 
Express using positive exponents, simplify if possible.

(A over 2)^-4.

(A/2)^-4
A negative exponent means take the inverse of the base (by definition).
(A/2) is the base; -4 is the exponent.
After a few moves, both A and 2 become bases:

(A/2)^-4
Distribute the exponent to numerator and denominator:
= (A^-4) / (2^-4)
Take the inverse of each:
= (1/A^4) / (1/2^4)
= (1/A^4) / (1/16)
Invert the denominator and multiply (a shortcut):
= (1/A^4)(16/1)
= 16/(A^4)

Alternately, flip the fraction and change the sign of the exponent (yet another shortcut):
(A/2)^-4
= (2/A)^4

Distribute the exponent:
= 16/(A^4)

Providing I have not made a mistake, you can see there is more than one way to do this.

The first part, where the sign of the exponent changes, follows from the definition of a negative exponent.

The second part, turning division of a fraction by a fraction, is derived easily by a few intermediate steps.

You can ask about that in another question.
 
You must log in or register to reply here.
Top