Question

Explain me PLEASEEEE!!!

Answer 1

`((a^(2))^(3).a^(-3))/(a^(10))=(a^(6).a^(-3))/(a^(10))=(a^(3))/(a^(10))=a^(-7)=(1)/(a^(7))`

Explanation:

Let us revise the properties of exponents

• 
  `a^(m).a^(n)=a^(m+n)`

• 
  `(a^(m))/(a^(n))=a^(m-n)`

• 
  `(a^(m))^(n)=a^(m.n)`

• 
  `a^(-m)=(1)/(a^(m) )`

Let us use these properties to solve the question

→ By using the 3rd property above

∵
`(a^(2))^(3)=a^(2.3)=a^(6)`

∴
`((a^(2))^(3).a^(-3))/(a^(10))=(a^(6).a^(-3))/(a^(10) )`

→ By using the 1st property above

∵
`a^(6).a^(-3)=a^(6+-3)=a^(6-3)=a^(3)`

∴
`((a^(2))^(3).a^(-3))/(a^(10))=(a^(6).a^(-3))/(a^(10))=(a^(3))/(a^(10))`

→ By using the 2nd property above

∵
`(a^(3))/(a^(10))=a^(3-10)=a^(-7)`

∴
`((a^(2))^(3).a^(-3))/(a^(10))=(a^(6).a^(-3))/(a^(10))=(a^(3))/(a^(10))=a^(-7)`

→ By using the 4th property above

∵
`a^(-7)=(1)/(a^(7))`

∴
`((a^(2))^(3).a^(-3))/(a^(10))=(a^(6).a^(-3))/(a^(10))=(a^(3))/(a^(10))=a^(-7)=(1)/(a^(7))`