Question

Hello, is it possible to show me the steps to solve this answer? I am unsure as to why I got it wrong.

Answer 1

Given:

`((5e^(-3))/(2e^(18)e^(-13)))^(-4)`

Required:

We need to simplify the given expression.

Step-by-step explanation:

`Use\text{ }((a)/(b))^n=(a^n)/(b^n).`

`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=((5e^(-3))^(-4))/((2e^(18)e^(-13))^(-4))`
`Use\text{ }(ab)^n=a^nb^n,\text{ and }(a^n)^m=a^(n* m).`

`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=\frac{5^(-4)e^(-3*(-4))}{{2^(-4)e^(18*(-4))e^(-13*(-4))}}`
`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=\frac{5^(-4)e^(12)}{{2^(-4)e^(-72)e^(52)}}`

`Use\text{ }a^na^m=a^(n+m).`

`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=\frac{5^(-4)e^(12)}{{2^(-4)e^(-72+52)}}`

`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=\frac{5^(-4)e^(12)}{{2^(-4)e^(-20)}}`
`Use\text{ }(1)/(a^(-n))=a^n\text{ and }a^(-n)=(1)/(a^n).`

`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=\frac{2^4e^(12)e^(20)}{{5^4}}`
`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=\frac{2^4e^(12+20)}{{5^4}}`
`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=\frac{2^4e^(32)}{{5^4}}`
`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=(16e^(32))/(625)`

Final answer:

`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=(16e^(32))/(625)`

Alternate method:

`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=((2e^(18)e^(-13))/(5e^(-3)))^4`

`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=((2e^(18-13))/(5e^(-3)))^4`

`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=((2e^5)/(5e^(-3)))^4`

`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=((2e^5e^3)/(5))^4`

`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=((2e^(5+3))/(5))^4`

`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=((2e^8)/(5))^4`

Final answer:

`((5e^(-3))/(2e^(18)e^(-13)))^(-4)=(16e^(32))/(625)`