Question

Describe how (2 ^ 3)(2 ^ - 4) can be simplified . Multiply the bases and add the exponents. Then find the reciprocal and change the sign of the exponent . The same base and add the exponents . Then multiply by - 1 . The base and multiply the exponents . Then multiply by -1 Add the exponents and keep the same base Then find the reciprocal and change the sign of the exponent .

Answer 1

Answer:

Add the exponents and keep the same base Then find the reciprocal and change the sign of the exponent .

Step-by-step explanation:

Given the expression  (2^3)(2^- 4), we will apply the law of indices below to solve the equation;

$a^m \times a^n = a^{m+n}\\a^{-m} =\frac{1}{a^m}$

Applying this on the given expression;

$(2 ^ 3)(2 ^{-4})$

Step 1: Add the exponents and keep the same base as shown;

$= (2 ^ 3)(2 ^{-4})\\\\= 2^{3+(-4)}\\\\ = 2^{3-4}\\\\= 2^{-1}$

Step 2: Find the reciprocal and change the sign of the exponent

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