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simplify the following expression.4^3 • 4^-5

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2 Answers

Another way to think about it, and yet another rule of exponents, is that xa*xb=xa+b (it's the flipped version of what Phillip had said).
 
Thus 43*4-5=43+(-5)=43-5=4-2.
43*4-5
 
To simplify this, you'll need two rules of exponents.  The first rule is that 4-5 = 1/45, so we can re-write the expression as:
 
43/45
 
The second rule is that xa/xb = xa-b, so:
 
43/45 = 43-5 = 4-2 = 1/42 = 1/16
 
Another way to think of it is:
 
43/45 = (4*4*4)/(4*4*4*4*4) = 1/(4*4) = 1/16