How do you simplify #(\frac { a ^ { 2x } } { a ^ { 3} } ) ^ { 3} #?

1 Answer
Ben
Jun 7, 2018

Distribute the exponent to the top and bottom terms of the fraction, then subtract the exponent in the denominator from that in the numerator to get #a^(6x-9)#

Explanation:

First, we'll apply the exponent to the terms inside of the parentheses:

#((a^(2x))/(a^3))^3=((a^(2x))^3)/((a^3)^3)#

Next, we'll simplify the expressions in the numerator and denominator. Remember, an exponent raised to another exponent is the same as multiplying the two exponents together:

#((a^(2x))^3)/((a^3)^3)=(a^(6x))/(a^9)#

Finally, since we're dividing two exponents with the same base, we can simplify by saying that its equivalent to the difference between the two exponents:

#(a^(6x))/(a^9)=a^(6x-9)#

And now it's as simplified as it can be:

#color(green)(a^(6x-9))#

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