Question

Simplify the expression so there is only one positive power for each base 2.7^-3 * 3.8^2 *2.7^4 * 3.8^3

Answer 1

Answer:

$2.7\times 3.8^5$

Step-by-step explanation:

Given expression is,

$2.7^{-3}\times 3.8^{2}\times 2.7^4\times 3.8^3$

Using the product rule of exponent i.e. $a^ma^n=a^{m+n}$

$=2.7^{-3+4}\times 3.8^{2+3}$

$=2.7^{1}\times 3.8^{5}$

$=2.7\times 3.8^5$

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,

$2.7\times 3.8^5$

Answer 2

$2.7^{-3}\cdot3.8^2\cdot2.7^4\cdot3.8^3\\\\=(2.7^{-3}\cdot2.7^4)\cdot(3.8^2\cdot3.8^3)\qquad|\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=2.7^{-3+4}\cdot3.8^{2+3}\\\\=2.7^1\cdot3.8^5$