Question

How do you simplify `(\frac { a ^ { - 2} b ^ { - \frac { 1} { 4} } c ^ { 3} } { a ^ { - \frac { 1} { 2} } b ^ { \frac { 3} { 6} } c ^ { 0} } ) ^ { 4}`?

Answer 1

The expression simplifies to

`(c^12)/(a^6  b^3)`

also written as  `a^(-6)  b^(-3)  c^12`

Explanation:

Simplify

`((a^(−2)   b^(-(1)/(4))  c^3)/(a^(−(1)/(2))    b^((3)/(6))    c⁰))^4`

1) Clear the parentheses by multiplying every single exponent inside the parentheses by the exponent outside -- which is `4`

`(a^(−8)   b^(-(4)/(4))  c^12)/(a^(−(4)/(2))   b^((12)/(6))    c⁰)`

2) Reduce the fractional exponents to lowest terms

`(a^(−8)   b^(-1)   c^12)/(a^(−2)   b^2   c⁰)`

3) Get rid of the negative exponents by flipping them to the other side of the fraction bar and making them positive

`(a^2   c^12)/(a^8   (b^2)(b^1)     c^0)`

4) Write `b^1` as `b`, and write `c⁰` as `1`, then multiply

`(a^2   c^12)/(a^8   b^3)`

5) Reduce `(a^2)/(a^8)   "to"   (1)/a^6`

`(c^12)/(a^6  b^3)` `larr` answer

6) If you want an expression that isn't a fraction, you can get rid of the denominator by flipping the numbers into the numerator and changing the signs of their exponents

`a^(-6)  b^(-3)  c^12` `larr` same answer