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)
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
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.
To simplify the expression, we can apply the rules of exponents. Here are the steps:
Step 1: Simplify each exponent separately.
3 to the power of (-4) = 1/3 to the power of 4
2 to the power of 3 = 8
3 to the power of 2 = 9
2 to the power of 4 = 16
3 to the power of (-3) = 1/3 to the power of 3
Step 2: Rewrite the expression using the simplified exponents.
[(1/3)^4 * 8 * 9] / [16 * (1/3)^3]
Step 3: Simplify the expression further.
[(1/81) * 8 * 9] / [16 * (1/27)]
Step 4: Simplify the numerator and denominator separately.
(8 * 9) / (16 * (1/3))
Step 5: Simplify the multiplication.
72 / (16 * (1/3))
Step 6: Simplify the denominator.
72 / (16/3)
Step 7: Divide by multiplying the numerator by the reciprocal of the denominator.
72 * (3/16) = 9/4
The simplified expression is 9/4.
To simplify the given expression, we need to use the properties of exponents.
First, let's simplify each individual term:
3 to the power of -4 = 1/(3^4) (negative exponent means reciprocal)
2 to the power of 3 = 2^3
3 to the power of 2 = 3^2
2 to the power of 4 = 2^4
3 to the power of -3 = 1/(3^3) (negative exponent means reciprocal)
Now, let's substitute these simplified values back into the expression:
(1/(3^4)) * (2^3) * (3^2) / (2^4) * (1/(3^3))
Next, let's combine the same bases:
- For the numerator, we have (2^3) * (3^2) = 8 * 9 = 72.
- For the denominator, we have (2^4) * (1/(3^3)) = 16 * (1/27) = 16/27.
Now, substitute these values back into the expression:
(1/(3^4)) * 72 / (16/27)
Next, let's simplify each fraction:
1/(3^4) = 1/81
72 / (16/27) = 72 * (27/16) = (72 * 27) / 16 = 1944/16 = 121.5
Finally, substitute these values back into the expression:
(1/81) * 121.5
Now, multiply the fractions:
1/81 * 121.5 = 121.5/81
This can be further simplified by dividing both numerator and denominator by their greatest common divisor, which is 27:
121.5/81 = (121.5/27) / (81/27) = 4.5/3
Therefore, the simplified expression for the given expression is 4.5/3, or equivalently, 3/2.