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

Hello, is it possible to show me the steps to solve this answer? I am unsure as to-example-1
User ShZ
by
5.9k points

1 Answer

1 vote

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)

User Nutters
by
6.5k points
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