9y2/3b-21y•b2-49y2/y b=20 y=4
To solve the expression \( \frac{9y^{2/3}b - 21y \cdot b^2 - 49y^2}{y} \) given \( b = 20 \) and \( y = 4 \), we'll start by substituting the values of \( b \) and \( y \) into the expression.
Substitute \( b = 20 \) and \( y = 4 \) into the expression:
\[ \frac{9(4)^{2/3}(20) - 21(4)(20^2) - 49(4^2)}{4} \]
Calculate each term step-by-step:
a. Calculate \( (4)^{2/3} \): \[ (4)^{2/3} = (2^2)^{2/3} = 2^{4/3} \approx 2.52 \text{ (keeping in mind decimal or exact form based on your preference)} \]
However, it's often easier to calculate it numerically: \[ (4)^{2/3} = 2^{4/3} = \sqrt[3]{16} \approx 2.52 \]
So: \[ 9(4)^{2/3}(20) \approx 9 \times 2.52 \times 20 = 453.6 \]
In exact form, \( 9 \cdot 2^{4/3} \cdot 20 \).
b. Calculate \( 21(4)(20^2) \): \[ 20^2 = 400 \] \[ 21(4)(400) = 33600 \]
c. Calculate \( 49(4^2) \): \[ 4^2 = 16 \quad \Rightarrow \quad 49(16) = 784 \]
Now substitute these calculated values into the expression:
\[ \frac{(9(4)^{2/3}(20)) - 33600 - 784}{4} \]
Substituting the one approximate number calculated above: \[ \frac{453.6 - 33600 - 784}{4} \]
In exact form: \[ \frac{(9 \cdot 2^{4/3} \cdot 20) - 33600 - 784}{4} \]
For combining, \( 33600 + 784 = 34384 \)
Final Steps: \[ \frac{(9(4)^{2/3}(20) - 34384}{4} \]
If working with approximation, further calculate \( (453.6 - 34384) \):
This is a very large negative number: \[ \approx \frac{-33930.4}{4} \approx -8482.6 \quad \text{(if using approximations)} \]
Thus in the end, we have our evaluated value. However, it might be required to show the final results in either exact or approximate form depending on the context.
If you need further clarifications or more specific steps, feel free to ask!
