Question

How do you rewrite ${( - 7)^{ - 1}}$ without the exponent?

Answer 1

In this question, ( - 7 ) is base and -1 is exponent.
Use the negative exponent law, ${a^{ - m}} = \dfrac{1}{{{a^m}}}$.

Complete step by step answer:
We know, ${a^{ - m}} = \dfrac{1}{{{a^m}}}$
Put a as $- 7$ and m as $- 1$
Putting the values in formula ${a^{ - m}} = \dfrac{1}{{{a^m}}}$
$\Rightarrow$ ${( - 7)^{ - 1}} = \dfrac{1}{{{{( - 7)}^1}}}$
$\Rightarrow$ $\dfrac{1}{{ - 7}}$
$\dfrac{1}{{ - 7}}$ can be written both ways $\dfrac{1}{{ - 7}}$ or $\dfrac{{ - 1}}{7}$

Thus, ${( - 7)^{ - 1}}$ rewrite without exponent is $\dfrac{1}{{ - 7}}$.

Additional information:
$\dfrac{1}{{ - 7}}$ can be written as decimal also .
Here, decimal value of $\dfrac{1}{{ - 7}}$ is $- 0.142...$
Whenever negative power comes you can solve the positive exponent and for negative you can take the reciprocal.
For example, in ${( - 7)^{ - 1}}$ solve it by assuming ${( - 7)^1}$ then take reciprocal of the obtained value like this
$=\dfrac{1}{{{{( - 7)}^1}}}$
Let’s take another example whose power is other than -1,
Solving ${( - 3)^{ - 2}}$ , firstly for this solve it by taking -2 as positive
$={( - 3)^2}$
$=( - 3) \times ( - 3)$
$=9$
Now reciprocal it
$=\dfrac{1}{9}$
Preferably use formula, so as to avoid confusion.
When an exponent is a negative number, the result is always a fraction. Infractions like this numerator are always 1 as we have to reciprocal the number.

Note: All the formulas should be known for solving this type of questions.
Positive and negative signs should be taken care of while solving this type of question.
When solving negative integers be careful about grouping, to avoid confusion use brackets that make your solution clear.