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

Question

please help me simplify this expression.

Answer 1

Another way to think about it, and yet another rule of exponents, is that x^a*x^b=x^a+b (it's the flipped version of what Phillip had said).

 

Thus 4³*4^-5=4^3+(-5)=4^3-5=4^-2.

Answer 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 x^a/x^b = x^a-b, so:

 

4³/4⁵ = 4^3-5 = 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