Can you simplify 2 to the third power times 2 to the fifth power?

1 Answer
Noah G
Jan 25, 2016

Yes, the exponential property #x^m#(#x^n#) = #x^(m + n)# can be used to simplify this problem.

Explanation:

#2^3#(#2^5#)

=#2^(5 + 3)#

= #2^8#

So, your problem can be simplified to #2^8#.

Beware that if you have an addition/subtraction (e.g #2^5# + #2^6#) you cannot simplify with this rule. With division you can, but you subtract exponents instead of adding them. Also, this rule only works if the bases are equal

Practice exercises:

  1. Simplify the following expressions. Beware of trick questions. When simplification is not possible, leave in exponential form.

a) #3^4 / 3^2#

b) #3^4(3^2)#

c) #3^4 - 3^2#

d) #3^4 / 3^-2#

e) #3^2(2^2)#

  1. Solve for x in #4^3 / 4^x = 4^10#. Hint: think of integer addition/subtraction rules.
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