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
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
To simplify the given expression, let's break it down step-by-step:
We have:
(3^-4) * (2^3) * (3^2) / (2^4) * (3^-3)
First, let's simplify the exponents:
(1/(3^4)) * (2^3) * (3^2) / (2^4) * (1/(3^3))
Next, apply the rule that a negative exponent is equal to the reciprocal of the positive exponent:
(1/(81)) * (2^3) * (9) / (16) * (1/(27))
Now, let's simplify the remaining powers:
(1/81) * (8) * (9) / (16) * (1/27)
Now, let's multiply and divide sequentially:
(8 * 9) / (81 * 16) * (1/27)
We get:
72 / 1296 * (1/27)
Next, let's simplify the fractions:
(2^3 * 9) / (6^4 * 16) * (1/27)
Now, multiply the numerators and denominators:
(72) / (5184) * (1/27)
Finally, simplify the fraction:
(72 * 1) / (5184 * 27)
Divide the numerator and denominator:
72 / 140,608
And simplify the fraction as much as possible:
3 / 5,024
Therefore, the simplified expression is 3/5024.