Question

How do you simplify `(1/4)^5•4^13`?

Answer 1

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`