According to the given expression, the value of b if [tex]b^2=b^{-10}\\[/tex] is -1 and + 1
Indices are expressed using exponents and bases. Some of the useful laws of indices are:
[tex]a^m\times a^n=a^{m+n}\\a^{-n}=\frac{1}{a^n}[/tex]
Given the expression;
[tex]b^2=b^{-10}\\[/tex]
This can also be expressed as:
[tex]b^2=\frac{1}{b^{10}}\\b^2 \times b^{10} =1\\b^{2+10} =1\\b^{12}=1\\b=\pm\sqrt[12]{1}\\b=\pm1[/tex]
Hence the value of b from the given indices is -1 and + 1
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