An expression has numbers, variables, and mathematical operations. The expression that is equivalent to (144a¹²b³)⁰°⁷⁵ is 2a³(9b³)⁰°⁷⁵.
<h3>What is an expression?</h3>
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression that is equivalent to
, this can be done in the following manner,
![\sqrt[4]{144a^{12}b^3}\\\\= \sqrt[4]{2^4 \times 3^2 \times a^{12} \times b^3}\\\\= (2^4 \times 3^2 \times a^{12} \times b^3)^{\frac14}\\\\= 2^{(\frac14 \times 4)} \times 3^{(\frac14 \times 2)} \times a^{(\frac14 \times 12)} \times b^{(\frac14 \times 3)}\\\\= 2 \times 3^{(\frac12)} \times a^{3} \times b^{(\frac34)}\\\\](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B144a%5E%7B12%7Db%5E3%7D%5C%5C%5C%5C%3D%20%5Csqrt%5B4%5D%7B2%5E4%20%5Ctimes%203%5E2%20%5Ctimes%20a%5E%7B12%7D%20%5Ctimes%20b%5E3%7D%5C%5C%5C%5C%3D%20%282%5E4%20%5Ctimes%203%5E2%20%5Ctimes%20a%5E%7B12%7D%20%5Ctimes%20b%5E3%29%5E%7B%5Cfrac14%7D%5C%5C%5C%5C%3D%202%5E%7B%28%5Cfrac14%20%5Ctimes%204%29%7D%20%5Ctimes%203%5E%7B%28%5Cfrac14%20%5Ctimes%202%29%7D%20%5Ctimes%20a%5E%7B%28%5Cfrac14%20%5Ctimes%2012%29%7D%20%5Ctimes%20b%5E%7B%28%5Cfrac14%20%5Ctimes%203%29%7D%5C%5C%5C%5C%3D%202%20%5Ctimes%203%5E%7B%28%5Cfrac12%29%7D%20%5Ctimes%20a%5E%7B3%7D%20%5Ctimes%20b%5E%7B%28%5Cfrac34%29%7D%5C%5C%5C%5C)
![= 2\times a^{3} \times 3^{(\frac12 \times \frac22)} \times b^{(\frac34)}\\\\= 2\times a^{3} \times 3^{(\frac24)} \times b^{(\frac34)}\\\\= 2\times a^{3} \times 9^{(\frac14)} \times b^{3(\frac14)}\\\\= 2\times a^{3} \times (9b^{3(\frac14)})\\\\=2a^3 \sqrt[4]{9b^3}](https://tex.z-dn.net/?f=%3D%202%5Ctimes%20a%5E%7B3%7D%20%20%5Ctimes%203%5E%7B%28%5Cfrac12%20%5Ctimes%20%5Cfrac22%29%7D%20%20%5Ctimes%20b%5E%7B%28%5Cfrac34%29%7D%5C%5C%5C%5C%3D%202%5Ctimes%20a%5E%7B3%7D%20%20%5Ctimes%203%5E%7B%28%5Cfrac24%29%7D%20%20%5Ctimes%20b%5E%7B%28%5Cfrac34%29%7D%5C%5C%5C%5C%3D%202%5Ctimes%20a%5E%7B3%7D%20%20%5Ctimes%209%5E%7B%28%5Cfrac14%29%7D%20%20%5Ctimes%20b%5E%7B3%28%5Cfrac14%29%7D%5C%5C%5C%5C%3D%202%5Ctimes%20a%5E%7B3%7D%20%20%5Ctimes%20%289b%5E%7B3%28%5Cfrac14%29%7D%29%5C%5C%5C%5C%3D2a%5E3%20%5Csqrt%5B4%5D%7B9b%5E3%7D)
Thus, The expression that is equivalent to (144a¹²b³)⁰°⁷⁵ is 2a³(9b³)⁰°⁷⁵.
Learn more about Expression:
brainly.com/question/13947055
Answer:
![y=-3,250t+25,000](https://tex.z-dn.net/?f=y%3D-3%2C250t%2B25%2C000)
Step-by-step explanation:
we know that
The linear equation in slope intercept form is equal to
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where
m is the slope of unit rate of the linear equation
b is the y-intercept or initial value of the linear equation
Let
t ----> the number of years since 2011
y --->the car's value
In this problem the year 2011 represent t=0
so
the year 2015, represent t=4 years (2015-2011)
we have the ordered pairs
(0,25,000) ----> represent the y-intercept
(4,12,000)
<em>Find the slope m</em>
The formula to calculate the slope between two points is equal to
substitute the values
---> is negative because is a decreasing function
we have
----> value of y when the value of x is equal to zero (initial value)
substitute the given values
![y=-3,250t+25,000](https://tex.z-dn.net/?f=y%3D-3%2C250t%2B25%2C000)
Answer:
tge answer is -8
Step-by-step explanation:
-14+8-5+8-2-3=-8
Answer:
0.487 kg
b.) the newborn weighs 0.487kg more than the weight predicted by the regression equation
Step-by-step explanation:
Given the Regression equation:
Weight = - 5.58 + 0.1686 length
Length of newborn = 48 cm
Actual Weight of newborn = 3kg
Predicted weight from regression model:
Weight = - 5.58 + 0.1686(48)
Predicted Weight = 2.513kg
Hence, residual = (Actual - predicted)
Residual = (3kg - 2.513kg) = 0.487kg
Since the actual weight is more or greater than the predicted weight:
b.) the newborn weighs 0.487kg more than the weight predicted by the regression equation
Answer:
erwreyhtrweqewrthyrtewe3
Step-by-step explanation:
q3wetrytrt432trytr423rer