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

The answer is in the picture

Answer 2

Answer: Hello!

The equation described is:

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

You can use the next relations to simplify it a bit:

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

$x^{a} *x^{b} = x^{a + b}$

Then our equation results in:

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

Then the correct answer is the first option.