[tex]2.7^{-3}\cdot3.8^2\cdot2.7^4\cdot3.8^3\\\\=(2.7^{-3}\cdot2.7^4)\cdot(3.8^2\cdot3.8^3)\qquad|\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=2.7^{-3+4}\cdot3.8^{2+3}\\\\=2.7^1\cdot3.8^5[/tex]
Answer:
[tex]2.7\times 3.8^5[/tex]
Step-by-step explanation:
Given expression is,
[tex]2.7^{-3}\times 3.8^{2}\times 2.7^4\times 3.8^3[/tex]
Using the product rule of exponent i.e. [tex]a^ma^n=a^{m+n}[/tex]
[tex]=2.7^{-3+4}\times 3.8^{2+3}[/tex]
[tex]=2.7^{1}\times 3.8^{5}[/tex]
[tex]=2.7\times 3.8^5[/tex]
In the above expression, power of 2.7 ( base ) is 1 and power of 3.8 is 5,
Also, 1 and 5 are positive numbers,
Hence, the required expression is,
[tex]2.7\times 3.8^5[/tex]
