How do you evaluate #\frac { 6^ { 5} \cdot 6^ { 5} } { ( 6^ { 4} ) ^ { 2} }#?

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Answer 1 · 2018-03-02T02:03:57

#36#

Recall the following property of exponents:

#x^a*x^b=x^(a+b)#

Multiplying two terms with the same base and different exponents yields that same term with the separate exponents added together.

So,

#(6^5*6^5)/(6^4)^2=6^(5+5)/(6^4)^2=6^10/(6^4)^2#

Recall that #(x^a)^b=x^(ab)#

Applying this property, we get

#6^10/(6^4)^2=6^10/(6^(4*2))=6^10/6^8#

Recall that #x^a/x^b=x^(a-b)#

Dividing two terms with the same base and different exponents yields that same term with the separate exponents subtracted from one another.

#6^10/6^8=6^(10-8)=6^2=36#