Question

Choose the incorrect options.

• A. $x^{-4}\times x^{-2}=x^8$
• B. $\frac{x^5}{x^3}=x$
• C. $(x^2{)}^4=x^{2^4}$
• D. $2x^{-1}=\frac{1}{2x}$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $x^{-4}\times x^{-2}=x^8$
B $\frac{x^5}{x^3}=x$
C $(x^2{)}^4=x^{2^4}$
D $2x^{-1}=\frac{1}{2x}$

Since $a^m\times a^n=a^{m+n}$ for a non-zero integer $a$ and integers $m$ and $n,$
$x^{-4}\times x^{-2}=x^{-4-2}=x^{-6}\ne x^8$ in general.

Since $\frac{a^m}{a^n}=a^{m-n}$ for a non-zero integer $a$ and integers $m$ and $n,$
$⟹\frac{x^5}{x^3}=x^{5-3}=x^2\ne x$ in general.

Using the law $(a^m{)}^n=a^{mn},$
$(x^2{)}^4=x^{2\times 4}=x^8\ne x^{16}$ in general.

Using the law $a^{-m}=\frac{1}{a^m},$
$2x^{-1}=2\times \frac{1}{x}=\frac{2}{x}\ne \frac{1}{2x}$ in general.

Hence, the calculations in all the given options are wrong.