Evaluate #4(1/3)^7 div 2(1/3)^3# ?

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Answer 1 · 2017-12-06T05:45:40

The expression simplifies to #(2)/(81)#

It looks like the #4# and the #2# are coefficients.

#4((1)/(3))^7 -: 2((1)/(3))^3#

1) Using a calculator, evaluate the fractions raised to the power of #7# and the power of #3#

#4((1)/(2187)) -: 2((1)/(27))#

2) Clear the parentheses by distributing the coefficients

#(4)/(2187) -: (2)/(27)#

3) Divide the fractions by multiplying by the reciprocal of the divisor

#(4)/(2187) xx (27)/(2)#

4) Reduce the fraction to lowest terms

#cancel(4)^2/cancel(2187)^81 xx cancel(27)^1/cancel(2)^1#

5) The fractions reduce to

#(2)/(81) xx (1)/(1)#

Answer:

#(2)/(81)#

Answer 2 · 2017-12-06T05:46:42

#2/81#

Expression #=4(1/3)^7 div 2(1/3)^3#

To make this clearer, let's rewrite the expression as follows:

Expression#= (4xx(1/3)^7)/(2xx(1/3)^3) = 2xx((1/3)^7)/((1/3)^3) #

Now we can use the law of exponents that states:

#(a^m)/(a^n) = a^(m-n)#

Thus, Expression #=2xx (1/3)^(7-3)#

#= 2xx(1/3)^4#

#=2/3^4 = 2/81#