Question

Simplify the following expression.

A.49
B.1/14
C.1/49
D.14

Answer 1

C

Explanation:

Using the rules of exponents

•
`a^(m)` ×
`a^(n)` ⇔
`a^((m+n))`

•
`a^(-m)` ⇔
`(1)/(a^(m) )`

Hence

`7^(-5/6-7/6)` =
`7^{-(12)/(6) }` =
`7^(-2)`, then

`7^(-2)` =
`(1)/(7^(2) )` =
`(1)/(49)` → C

Answer 2

C. 1/49

EXPLANATION

The given expression is

`{7}^{ - (5)/(6) } * {7}^{ - (7)/(6) }`

Recall that:

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

We apply this product rule of exponents to get:

`{7}^{ - (5)/(6) } * {7}^{ - (7)/(6) } = {7}^{ - (5)/(6) + - (7)/(6) }`

This implies that:

`{7}^{ - (5)/(6) } * {7}^{ - (7)/(6) } = {7}^{ - (12)/(6) }`

`{7}^{ - (5)/(6) } * {7}^{ - (7)/(6) } = {7}^( - 2)`

Recall again that:

`{a}^( - m) = \frac{1}{ {a}^(m) }`

We apply this rule to get:

`{7}^{ - (5)/(6) } * {7}^{ - (7)/(6) } = \frac{1}{ {7}^(2) }`

This simplifies to:

`{7}^{ - (5)/(6) } * {7}^{ - (7)/(6) } = (1)/(49)`