Question

h) n) c ) i) o)
ajutațima va rog​

Answer 1

$h) \; \dfrac{9^{-2} \cdot 27}{3^4} = \dfrac{\big(3^2\big)^{-2} \cdot 3^3}{3^4}=\dfrac{3^{-4} \cdot 3^3}{3^4}=\dfrac{3^{-4}}{3} = \dfrac{1}{3^{1-(-4)}}= \red{ \dfrac{1}{243}} \\\;$

$n)\; \dfrac{18 \cdot 9^3}{3^{12}}= \dfrac{18\cdot \big( 3^2\big)^3}{3^{12}}=\dfrac{18 \cdot 3^6}{3^{12}}=\dfrac{18}{3^6} = \dfrac{18}{729}^{(9}=\red{\dfrac{2}{81}}\\\;$

$c)\; \dfrac{64 \cdot 4^5}{16^4}= \dfrac{4^3 \cdot 4^5}{\big(4^2\big)^4}=\dfrac{4^{3+5}}{4^{2\cdot 4}}= \dfrac{4^8}{4^8}=\red{1}\\\;$

$i)\; \dfrac{4 \cdot 2^{-3}}{16 \cdot 2^{-5}}=\dfrac{4 \cdot 2^{-3-(-5)}}{16}=\dfrac{4 \cdot 2^2}{16}^{(4}= \dfrac{2^2}{4}=\dfrac{4}{4}=\red{1}\\\;$

$o)\; \dfrac{125^5 \cdot 5^5}{25^4}=\dfrac{\big(5^3 \big)^5\cdot 5^5}{\big(5^2 \big)^4}=\dfrac{5^{15} \cdot 5^5}{5^8}=\dfrac{5^{20}}{5^8}=\red{5^{12}}$