Answer
$\dfrac{0.16}{x^4}$
Work Step by Step
RECALL:
(i) $(a^m)^n = a^{mn}$
(ii) $(ab)^m=a^mb^m$
(ii) $a^m \cdot a^n =a^{m+n}$
(iv) $a^0=1, a\ne0$
(v) $a^{-m} = \dfrac{1}{a^m}$
Use rule (i) and rule (ii) above to obtain:
$=2^2x^{-3\cdot2} \cdot 0.2^2x^2
\\=4x^{-6} \cdot 0.04x^2
\\=0.16x^{-6} \cdot x^2$
Use rule (iii) above to obtain:
$=0.16x^{-6+2}
\\=0.16x^{-4}$
Use rule (v) above to obtain:
$=0.16 \cdot \dfrac{1}{x^4}
\\=\dfrac{0.16}{x^4}$
