Question

Simplify3³×9²×125³÷9³

Answer 1

Explanation:

Prime factorize 9 and 125

9 = 3* 3 = 3²

125 = 5 * 5 * 5 = 5³

3³ * 9² * 125³ ÷ 9³ =
`(3^(3)*(3^(2))^(2)*(5^(3))^(3))/((3^(2))^(3))\\`

`= (3^(3)*3^(4)*5^(9))/(3^(6))\\\\=(3^(3+4)*5^(9))/(3^(6))\\\\= (3^(7)*5^(9))/(3^(6))\\\\=3^(7-6)*5^(9)\\=3*5^(9)`

Exponent laws:

`(a^(m))^(n)=a^(m*n)\\\\\\a^(m)*a^(n) = a^(m +n)\\\\\\(a^(m))/(a^(n))=a^(m-n) \ ; \ m > n`