## Algebra 1

$\dfrac{0.16}{x^4}$
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: $=0.16 \cdot \dfrac{1}{x^4} \\=\dfrac{0.16}{x^4}$