Question

How do you express $2{{x}^{-2}}$ with positive exponents?

Answer 1

Hint: (1) In this question, the expression given to us is a negative exponent.
(2) If $n$ is a positive integer and $a\ne 0,$ then ${{a}^{-n}}=\dfrac{1}{{{a}^{n}}}$
(3) The negative exponent tells us to rewrite the expression by taking the reciprocal of the base and then changing the sign of exponent.
(4) Any expression that has negative exponents is not considered to be in simplest form.
(5) We will use the definition of negative exponent and other properties of exponents to write an expression with only positive exponents.

Complete step by step solution:
We have to express $2{{x}^{-2}}$ with a positive exponent.
$2{{x}^{-2}}$ is a negative exponent.
Here $2$ is a positive integer and $2\ne 0$
Using the definition of negative exponent
${{a}^{-n}}=\dfrac{1}{{{a}^{n}}}$
So, our answer on simplifying will be,
$2{{x}^{-2}}=\dfrac{2}{{{x}^{2}}}$

So, $2{{x}^{-2}}$ with positive exponents will be $\dfrac{2}{{{x}^{2}}}$.

Note: (1) When simplifying an expression with exponents. We must be careful to correctly identify the base that is raised to each exponent.
(2) Apply the negative exponent rule ${{a}^{-n}}=\dfrac{1}{{{a}^{n}}}$
(3) Negative exponent rule says that negative exponents in the numerator get moved to the denominator and become positive exponents.
(4) Negative exponents in the denominator get moved to the numerator and become positive exponents.
(5) Only move the negative exponents.
(6) Note that the order in which things are moved does not matter.