CPM Homework Help : CCA2 Problem 7-27

Compute without a calculator Mr. Keis wrote the following problem on the board and told his class, “No calculators please. Simplify. You have sixty seconds!”

$( \frac { 13 ^ { 12 } } { 14 ^ { 23 } } ) ( \frac { 27 ^ { 3 } } { 13 ^ { 11 } } ) ( \frac { 2 ^ { 10 } } { 27 ^ { 4 } } ) ( \frac { 14 ^ { 22 } } { 13 } ) ( \frac { 27 } { 2 ^ { 9 } } )$

Time yourself and simplify the expression. Did you meet the challenge?

Hint:

Remember the properties of exponents:
$a^b\cdot a^c=a^{b+c}$
$\frac{a^b}{a^c}=a^{b-c}$

More Help:

Focus on each base one at a time.
$\frac{13^{12}}{13^{11 + 1}} = 1\:\:\:\:\:\frac{27^{3 + 1}}{27^4} = 1\:\:\:\:\:\frac{2^{10}}{2^9} = 2\:\:\:\:\:\frac{14^{22}}{14^{23}} = \frac{1}{14}$

Answer:

$\frac{1}{7}$