How do you multiply #(x ^ { 2} y ^ { - 2} ) ^ { 3} \cdot - x ^ { 2} y ^ { 0}#?

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Answer 1 · 2017-08-07T02:35:53

Expresion #= -x^8/y^6#

Expresion #=(x^2y^-2)^3 * -x^2y^0#

To simplify this expression we will use the following laws of indicies:

(i) #a^m xx a^n = a^(m+n)#

(ii) #(a^m)^n = a^(m xx n)#

(iii) #a^0 =1#

(iv) #a^-m = 1/a^m#

Applying (iii) to the second term of the product:

#-x^2y^0 = - x^2*1#

Hence, Expression #= (x^2y^-2)^3 * (-x^2)#

Applying (ii):

Expression #= x^6y^-6 * (-x^2)#

Applying (iv):

Expression #= -x^2 * x^6/y^6#

Finally, applying (i):

Expression #= -x^8/y^6#