Question

Which is equivalent

Answer 1

D

Explanation:

Using the rules of exponents

•
`a^(-m)` ⇔
`(1)/(a^(m) )`

•
`a^{(1)/(2) }` ⇔
`√(a)`

Hence

`36^{-(1)/(2) }` =
`\frac{1}{36^{(1)/(2) } }` =
`(1)/(√(36) )` =
`(1)/(6)`

Answer 2

For this case we must find an expression equivalent to:

`36 ^ {- \frac {1} {2}}`

By definition of power properties we have to:

`a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}`

So, rewriting the expression we have:

`\frac {1} {36 ^ {\frac {1} {2}}}=`

By definition of power properties we have to:

`\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}`

So:

`\frac {1} {\sqrt {36}} =\\\frac {1} {\sqrt {6 ^ 2}} =\\\frac {1} {6}`

Answer:

Option D