How do you simplify #\frac { 3^ { 9} \cdot 3^ { 7} } { ( 3^ { 3} ) ^ { 4} }#?

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Answer 1 · 2017-02-22T20:08:41

#3^4#

Using Law of addition of exponents in the numerator and law of multiplication of exponents in the denominator, it is
#(3^16)/3^12#

Next using law of subtraction of exponents, it is=#3^(16-12)= 3^4#

Answer 2 · 2017-02-22T20:09:02

#81#

Some rules to take note of:

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

#(a^b)^c = a^(b*c)#

#(a^b)/(a^c) = a^(b-c)#

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So now, let's apply them:

#(3^9*3^7)/((3^3)^4)#

Using the first rule, simplify the numerator.

#(3^16)/((3^3)^4)#

Now apply the second rule to the denominator.

#(3^16)/(3^12)#

Finally, apply the third rule to the entire fraction.

#3^4#

To get the final answer, do the operation:

#3*3*3*3 = 81#