Question

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

Answer 1

`36`

Explanation:

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`