How do you simplify $(1/4)^5•4^13$ ?

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Answer 1 · 2016-07-17T21:31:37

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

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

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

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

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: $color(green)( 65 137/256$

How do you simplify (1/4)^5•4^13 (1/4)^5•4^13?