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

$\because a^m\times a^n=a^{m+n}$

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

$a^{-m}=\frac{1}{a^m}$

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

$\because2^{x-1}=2^x\times2^{-1}$

We used the first rule above

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

$2^{-1}=\frac{1}{2^1}=\frac{1}{2}$

Then the answer will be

$2^{x-1}=\frac{1}{2}.2^x$

Answer a.