How do you simplify # (1/4)^5•4^13#?

1 Answer
Jul 17, 2016

Answer:

Improper fraction: #color(green)(16777/256#

Mixed fraction: #color(green)( 65 137/256#

Explanation:

Note that #(a/b)^x = (a^x)/(b^x)#

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#(1/4)^5 * 4^13#

Follow the rule from above and apply it to the first term.

#1^5/4^5 * 4^13#

#(1*1*1*1*1)/(4*4*4*4*4) * 4^13#

#1/1024 * 4^13#

Now evaluate the second term.

#1/1024 * (4*4*4*4*4*4*4*4*4*4*4*4*4)#

#1/1024 * 67108864#

Rewrite as fractions and multiply.

#1/1024 * 67108864/1#

#(1times67108864)/(1024times1)#

#67108864/1024#

Simplify the fraction.

Improper fraction: #color(green)(16777/256#

Mixed fraction: #color(green)( 65 137/256#