Question

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

geeeshhhh,
why not simply say:

(3^-4)(2^3)(3^2) / ( (2^4)(3^-3) )


we could just grind it out to get
(1/81)(8)(9) / ( (16)(1/27)
= (8/9) ÷ (16/27)
= (8/9)(27/16)
= 3/2

or, using exponent laws:
(3^-4)(2^3)(3^2) / ( (2^4)(3^-3) )
= 3^(-4 + 2 + 3) * 2(3 - 4)
= 3^1 * 2^-1
= 3/2