We know how to evaluate expressions like , and even But what if the power is negative? How would we evaluate for example?
To help us with that, let's go back to the results table for powers of
As we go down the list, the number in blue is divided by every time. If we follow the same pattern, we find that
Now, is just the reciprocal of So, raising a number to the power of is the same as finding its reciprocal!
Express as a fraction in its simplest form.
The expression means the reciprocal of . Hence
$7^{-1}=$
|
a
|
$-\dfrac{1}{7}$ |
|
b
|
$(-7)^1$ |
|
c
|
$-1$ |
|
d
|
$\dfrac{1}{7}$ |
|
e
|
$\dfrac{7}{1}$ |
$11^{-1}=$
|
a
|
$11$ |
|
b
|
$\dfrac{1}{11}$ |
|
c
|
$-11$ |
|
d
|
$-\dfrac{1}{11}$ |
|
e
|
$1$ |
What is
The expression means the reciprocal of Therefore,
What is $(-3)^{-1}?$
|
a
|
$-1$ |
|
b
|
${-3}$ |
|
c
|
$-\dfrac {1} {3}$ |
|
d
|
$\dfrac {1} {3}$ |
|
e
|
${3}$ |
What is $(-10)^{-1}?$
|
a
|
$-10$ |
|
b
|
$-1$ |
|
c
|
$-\dfrac{1}{10}$ |
|
d
|
$\dfrac{1}{10}$ |
|
e
|
$10$ |
Evaluate
The expression means the reciprocal of Therefore,
$\left(\dfrac{3}{2}\right)^{-1}=$
|
a
|
$\dfrac{1}{3}$ |
|
b
|
$-\dfrac{1}{3}$ |
|
c
|
$-\dfrac{3}{2}$ |
|
d
|
$-\dfrac{2}{3}$ |
|
e
|
$\dfrac{2}{3}$ |
$\left(\dfrac{4}{5}\right)^{-1}=$
|
a
|
$\dfrac{3}{4}$ |
|
b
|
$-\dfrac{4}{3}$ |
|
c
|
$-\dfrac{4}{5}$ |
|
d
|
$\dfrac{5}{4}$ |
|
e
|
$\dfrac{4}{5}$ |