Answer
Verified
420k+ views
Hint: We will use the laws of exponents. Exponents are better known as power or indices. The exponent of a variety says what percentage times to use the amount in multiplication.
Complete step-by-step solution -
We know that in an expression like ${{a}^{b}}$, a is called base and b is called power of the number.
Here, on comparing with ${{a}^{b}}$ we know that base is -2 and power is also -2.
Now according to law of exponents we know that: -
The exponents say how many times to use the number in multiplication.
A negative exponent means divides, because the opposite of multiplication is division.
A fraction exponent means taking root of the number.
Now since our power is negative, we will be using rule 2. For example, if we have ${{a}^{-b}}$ then this will evaluate to $\dfrac{1}{(a\times a\times a......btimes)}$. As ${{a}^{-b}}$ can be written as $1\times {{a}^{-b}}$ and therefore ${{a}^{-b}}$ is written as $\dfrac{1}{(a\times a\times a......btimes)}$.
So, according to rule 2 we will divide 1 by -2 two times.
${{(-2)}^{-2}}$= $\dfrac{1}{-2\times -2}$
We know that $-2\times -2=4$ because a negative number multiplied by a negative number of results in a positive number. So, the answer is
$\dfrac{1}{-2\times -2}$=$\dfrac{1}{4}$
Note: Now,if we talk about surds and indices there are several identities like
$\begin{align}
& {{x}^{1}}=x \\
& {{x}^{0}}=1 \\
& {{x}^{m}}\times {{x}^{n}}={{x}^{m+n}} \\
& {{({{x}^{m}})}^{n}}={{x}^{mn}} \\
& {{x}^{-n}}=\dfrac{1}{{{x}^{n}}} \\
\end{align}$
Which can be remembered as a formula to solve the question quickly.
Complete step-by-step solution -
We know that in an expression like ${{a}^{b}}$, a is called base and b is called power of the number.
Here, on comparing with ${{a}^{b}}$ we know that base is -2 and power is also -2.
Now according to law of exponents we know that: -
The exponents say how many times to use the number in multiplication.
A negative exponent means divides, because the opposite of multiplication is division.
A fraction exponent means taking root of the number.
Now since our power is negative, we will be using rule 2. For example, if we have ${{a}^{-b}}$ then this will evaluate to $\dfrac{1}{(a\times a\times a......btimes)}$. As ${{a}^{-b}}$ can be written as $1\times {{a}^{-b}}$ and therefore ${{a}^{-b}}$ is written as $\dfrac{1}{(a\times a\times a......btimes)}$.
So, according to rule 2 we will divide 1 by -2 two times.
${{(-2)}^{-2}}$= $\dfrac{1}{-2\times -2}$
We know that $-2\times -2=4$ because a negative number multiplied by a negative number of results in a positive number. So, the answer is
$\dfrac{1}{-2\times -2}$=$\dfrac{1}{4}$
Note: Now,if we talk about surds and indices there are several identities like
$\begin{align}
& {{x}^{1}}=x \\
& {{x}^{0}}=1 \\
& {{x}^{m}}\times {{x}^{n}}={{x}^{m+n}} \\
& {{({{x}^{m}})}^{n}}={{x}^{mn}} \\
& {{x}^{-n}}=\dfrac{1}{{{x}^{n}}} \\
\end{align}$
Which can be remembered as a formula to solve the question quickly.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE