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:
m<5 is 105
Step-by-step explanation:
<5 and <4 are alternate interior angles meaning they are congruent to each other.
Answer:
6 and 4
Step-by-step explanation: since it is "cm2" it means it was already halved. This means that the answer was originally 24, 6x4 is the only one that equals 24.