An expression is defined as a set of numbers, variables, and mathematical operations. The simplification of expression is 140(5x+4)¹⁵. Therefore, the correct option is A.
What is an Expression?
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression [tex]5\sqrt{2(5x+4)^{10}}\ \cdot 7\sqrt{2(5x+4)^{20}}[/tex] can be written as,
[tex]5\sqrt{2(5x+4)^{10}}\ \cdot 7\sqrt{2(5x+4)^{20}}\\\\= 5 \times 7 \times \sqrt{2} \times \sqrt{2} \times (5x+4)^{(10 \times \frac12)}}\times (5x+4)^{(20\times \frac12)}}\\\\=5 \times 7 \times 2 \times (5x+4)^{5}\times (5x+4)^{10}}\\\\= 140 (5x+4)^{(5+10)}\\\\= 140 (5x+4)^{15}[/tex]
Hence, the simplification of expression is 140(5x+4)¹⁵. Therefore, the correct option is A.
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