# Simplify the expression: (2^-1 + 2^-3)(8^1/3)

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Simplify the expression `(2^(-1)+2^(-3))(8^(1/3))` :

A property of exponents is that `a^(-m)=1/a^m` so `2^(-1)=1/2` and `2^(-3)=1/2^(3)=1/8` . `1/2+1/8=4/8+1/8=5/8` , so the expression in the parantheses is `5/8` .

`8^(1/3)=root(3)(8)=2`

**So we have `5/8*2=10/8=5/4` **

Given expression is `(2^-1+2^-3)(8^(1/3))` ........(1).

Now `2^-1=1/2` and `2^-3=1/2^3=1/8` .

So, `(1/2+1/8)=4/8+1/8=5/8`

and `(8^(1/3))=(2^3)^(1/3)=2` As `(a^m)^n=a^(mn)` .

So, expression (1) can be written as

(5/8)(2)=10/8=5/4. Answer.