Question

What is (9 − 2)^2)^4 / (4 + 3)^5 written in simplest form?

Answer 1

`([(9-2)^(2)]^(4))/((4+3)^(5) )` = 7³

Explanation:

Let us revise some rules of exponents

• 
  `a^(m)*a^(n)=a^(m+n)`

• 
  `(a^(m))/(a^(n))=a^(m-n)`

• 
  `(a^(m))^(n)=a^(mn)`

Let us use some of these rules to solve the question

∵ The expression is
`([(9-2)^(2)]^(4))/((4+3)^(5) )`

→ At first, simplify the bracket

∵ 9 - 2 = 7 and 4 + 3 = 7

∴
`([(9-2)^(2)]^(4))/((4+3)^(5) )` =
`([(7)^(2)]^(4))/((7)^(5) )`

→ Use the 3rd rule above to simplify the numerator

∵
`(7^(2))^(4)=7^((2)(4))`

∴
`([(7)^(2)]^(4))/((7)^(5) )` =
`(7^(8))/(7^(5))`

→ Use the 2nd rule above to simplify the result

∴
`(7^(8))/(7^(5))` =
`7^(8-5)` = 7³

∴
`([(9-2)^(2)]^(4))/((4+3)^(5) )` = 7³