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Exponents

Harder Examples

Example 8

Here are some harder examples, some of which use more than one of the rules we've learned so far.


(x^4*y^2)^3=(x^4)^3*(y^2)^3=x^(4*3)*y^(2*3)=x^12*y^6.

(a^3/(b^2*c^4))^3=((a^3)^3)/((b^2*c^4)^3)=(a^(3*3))/((b^2)^3*(c^4)^3)=a^9/(b^(2*3)*c^(4*3))=a^9/(b^6*c^12).


Exercise 8

Feeling confident about your skills with Exponents? Then try these harder examples. Once you are done, click on the question marks to see the solutions step-by-step:

(x*y^3*z^5)^(-7)
=1/(x*y^3*z^5)^7
=1/(x^7*(y^3)^7*(z^5)^7)
=1/(x^7*y^(3*7)*z^(5*7))
=1/(x^7*y^21*z^35).


=(b^(2*4)*c^(-2*4))/(a^(3*2)*b^2)
=(b^8*c^(-8))/(a^6*b^2)
(b^(8-2)*c^(-8))/a^6
=(b^6)/(a^6*c^8)


Summary

We summarise the rules of exponents:

Rule 1:        b^m*b^n=b^(m+n).

 

Rule 2:        b^m/b^n=b^m*b^(-n)=b^(m-n).

 

Rule 3:        (b^m)^n=b^(m*n)

 

Rule 4:        (a*b)^n=a^n*b^n

 

Rule 5:        (a/b)^n=a^n/b^n


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