Question

Which expression is equivalent to the expression shown 5^3^9 / 5^12

Answer 1

5^15

Explanation:

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Answer 2

For this case we must simplify the following expression:

`\frac {(5 ^ 3) ^ 9} {5 ^ {12}}`

By definition of power properties we have:

`(a ^ n) ^ m = a ^ {n * m}`

So, we can rewrite the expression as:

`\frac {5 ^ {3 * 9}} {5 ^ {12}} =\\\frac {5 ^ {27}} {5 ^ {12}} =`

By definition of division of powers of the same base we have:

`\frac {a ^ m} {a ^ n} = a ^ {m-n}`

So:

`5^( 27-12) = 5 ^ {15}`

Answer:

`5 ^ {15}`