The [tex]b^{-({2/d} )}[/tex] is equivalent to[tex]\frac{1}{(\sqrt[d]{b}) ^2}[/tex]
The given expression is,
[tex]b^{-({2/d} )}[/tex]
We solve the above expression by using the power rule
So,
What is the power rule for a¯ⁿ?
[tex]a^{-n} = \frac{1}{a^n}[/tex]
Therefore,
By using the above rule we get,
[tex]b^{-(2/d)} =\frac{1}{b^(2/d)}[/tex]
Remember that the power rule,
[tex]b^{(n/d)} =\sqrt[d]{({b})^{n}}[/tex].........(1)
Therefore,
By comparing with equation 1 we get,
[tex]\frac{1}{b^(2/d)}=\frac{1}{(d\sqrt{b})^{2} }[/tex]
Thus we get,
[tex]\frac{1}{b^(2/d)}=\frac{1}{(d\sqrt{a})^{2} }[/tex]
From the above expression
[tex]b^{-({2/d} )}[/tex]
is equivalent to,
[tex]\frac{1}{(d\sqrt{b) }^{2} }[/tex]
Therefor the option C is correct.
To learn more about the equivalent expression visit:
https://brainly.com/question/24734894
