Question

What is the simplified expression for,
3^negative 4 times 2^3 times 3^2 OVER 2^4 times 3^ negative 3?
THIS IS WRITTEN AS A FRACTION

3
-
2


3^2
______
2^2


3^2
_____
2


2^4
_____
3

Answer 1

Here are a few rules you need to know for this equation:

• Multiplying exponents of the same base: $x^m\times x^n=x^{m+n}$
• Dividing exponents of the same base: $\frac{x^m}{x^n}=x^{m-n}$
• Turning a negative exponent to a positive one: $x^{-m}=\frac{1}{x^m};\frac{1}{x^{-m}}=x^m$

So this is our algebraic expression: $\frac{3^{-4}\times 2^3\times 3^2}{2^4\times 3^{-3}}$

Firstly, multiply 3^-4 and 3^2: $\frac{3^{-4+2}\times 2^3}{2^4\times 3^{-3}}=\frac{3^{-2}\times 2^3}{2^4\times 3^{-3}}$

Next, divide:

$\frac{3^{-2}\times 2^3}{2^4\times 3^{-3}}=3^{-2-(-3)}2^{3-4}=3^12^{-1}$

Next, turn the negative exponent into a positive one: $3^12^{-1}= \frac{3}{2}$

Your final answer is 3/2, or 1.5.