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? (1 point)

Question

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

To simplify the expression, we can apply the laws of exponents.

First, let's simplify the numerator:
3^(-4) = 1/3^4 = 1/81
2^3 = 8
3^2 = 9

Now, let's simplify the denominator:
2^4 = 16
3^(-3) = 1/3^3 = 1/27

So, the expression simplifies to:
(1/81 * 8 * 9) / (16 * 1/27)

Now, let's simplify the expression further by multiplying the numerators and denominators:
(8 * 9) / (16 * 1/27)
= 72 / (16/27)

When we divide fractions, we multiply by the reciprocal of the second fraction:
= 72 * (27/16)
= 1944/16

Simplifying the fraction gives us:
= 121.5

Therefore, the simplified expression is 121.5.