Question

$\frac{1}{y^{-100}}=$ _____

• A. $y^{100}$
• B. $\frac{1}{y^{100}}$
• C. $y^{-100}$
• D. $-y^{100}$

Answer 1

The correct option is A $y^{100}$

For any non-zero integer 'a',
$a^{-m}=\frac{1}{a^m}$,
where 'm' is a positive integer.
$\Rightarrow a^m=\frac{1}{a^{-m}}$
or, $\frac{1}{a^{-m}}=a^m$

Comapring $\frac{1}{y^{-100}}$ with the above, we get,
$\frac{1}{y^{-100}}=y^{100}$


Alternately,

Since $a^{-m}=\frac{1}{a^m}\text{or}{a}^m=\frac{1}{a^{-m}},$

$\frac{1}{y^{-100}}=\frac{1}{\left(\frac{1}{y^{-(-100)}}\right)}$

$=\frac{1}{\left(\frac{1}{y^{100}}\right)}$

$=\frac{1}{y^{100}}$