Question

Question 7 (Worth 1 points) (01.03 MC) What is the simplified expression for 3 to the power of negative 4 multiplied by 2 to the power of 3 multiplied by 3 to the power of 2 whole over 2 to the power of 4 multiplied by 3 to the power of negative 3? 3 over 2 3 to the power of 2 over 2 to the power of 2 3 to the power of 2 over 2 2 to the power of 4 over 3

Answer 1

Answer:

3 over 2

Step-by-step explanation:

Given the expression

$\frac{3^{-4} \times 2^3 \times 3^2}{2^4 \times 3^{-3}}$

Using the law of indices to simplify

$= \frac{3^{-4} \times 3^2 \times 2^3}{2^4 \times 3^{-3}}\\= \frac{3^{-4+2} \times 2^3}{2^4 \times 3^{-3}}\\= \frac{3^{-2} \times 2^3}{2^4 \times 3^{-3}}\\= \frac{3^{-2}}{3^{-3}} \times \frac{2^3}{2^4} \\= 3^{-2+3} \times 2^{3-4}\\= 3^1 \times 2^{-1}\\= 3 \times \frac{1}{2}\\= \frac{3}{2}$

Hence option A is correct 3 over 2