An expression has numbers, variables, and mathematical operations. The expression that is equivalent to (144a¹²b³)⁰°⁷⁵ is 2a³(9b³)⁰°⁷⁵.
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 [tex]\sqrt[4]{144a^{12}b^3}[/tex], this can be done in the following manner,
[tex]\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)}\\\\[/tex]
[tex]= 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}[/tex]
Thus, The expression that is equivalent to (144a¹²b³)⁰°⁷⁵ is 2a³(9b³)⁰°⁷⁵.
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