The expression B. [tex]\frac{1}{9^{16} }[/tex] is equivalent to [tex](9^{-2}) ^{8} .[/tex]
Step-by-step explanation:
Step 1:
For the given number, -2 and 8 are both exponents.
According to the power rule, [tex](a^{x}) ^{y} = a^{xy}[/tex].
Here a is 9, x is -2 and y is 8.
Substituting the values, we get [tex](9^{-2}) ^{8} = 9^{(-2)(8)} .[/tex]
[tex]9^{(-2)(8)} = 9^{-16} .[/tex]
Step 2:
According to the negative exponent rule, we have [tex]a^{-z} = \frac{1}{a^{z} } .[/tex]
Here a is 9 whereas z is equal to 16.
So [tex]9^{-16} = \frac{1}{9^{16} } .[/tex]
This is represented by option B.
