Question

Which expression is equivalent to 2x-1? a. 2 b. b. c. 2. 2x d. 2* 2x - 1 / 1

Answer 1

Let us revise some rules of exponents

`\because a^m* a^n=a^(m+n)`

If we have two equal bases multiply by each other then we add their exponent like the rule above

`a^(-m)=(1)/(a^m)`

If a base has a negative exponent, then we can change the exponent to positive by reciprocal the base as the rule above

Let us use these 2 rules to solve the question

`\because2^(x-1)=2^x*2^(-1)`

We used the first rule above

Now we can change the exponent -1 by 1 using the 2nd rule above

`2^(-1)=(1)/(2^1)=(1)/(2)`

Then the answer will be

`2^(x-1)=(1)/(2).2^x`

Answer a.