Question

Помогите, пожалуйста, упростить выражения с объяснением 144-148!!!!

Answer 1

Формулы со степенями на картинке

$144) \ b^\sqrt{3}}* (\frac{1}{b} )^{\sqrt{3} -1}=b^\sqrt{3}}* b ^{-(\sqrt{3}-1) }=b^\sqrt{3}}* b ^{1-\sqrt{3} }=b^{\sqrt{3}+1-\sqrt{3}}=b \\ \\ 145) \ b^{1.2}*b^{1.8}:b^2=b^{1.2+1.8-2}=b^1=b \\ \\ 146) \ ( \frac{1}{x})^{\sqrt{2} -1}*x^{\sqrt{2}} :x^{-4}=x^{1-\sqrt{2} }*x^{\sqrt{2}} :x^{-4}=x^{1-\sqrt{2}+\sqrt{2} -(-4)}=x^5 \\ \\ a^{\sqrt{2} }* ( \frac{1}{a})^{\sqrt{2} -1}=a^{\sqrt{2} }* a^{1-\sqrt{2} }=a^{\sqrt{2} +1-\sqrt{2} }=a \\ \\ (a^{\sqrt{3}} )^{\sqrt{3}}=a^{\sqrt{3}*\sqrt{3}}=a^3$

Answer 2

144) b^{\sqrt{3}}*(\frac{1}{b})^{\sqrt{3}-1}=b^{\sqrt{3}}*b^{1-\sqrt{3}}=b^{\sqrt{3}+1-\sqrt{3}}=b\\\\145) b^{1,2}*b^{1,8}:b^{\frac{3{2}}=b^{1,2}*b^{1,8}:b^{1,5}=b^{1,2+1,8-1,5}=b^{1,5}\\\\146) (\frac{1}{x})^{\sqrt{2}-1}*x^{\sqrt{2}}:x^{-4}=x^{1-\sqrt{2}}*x^{\sqrt{2}}:x^{-4}=x^{1-\sqrt{2}+\sqrt{2}+4}=x^{5}\\\\147) a^{\sqrt{2}} *(\frac{1}{a})^{\sqrt{2}-1} =a^{\sqrt{2}}*a^{1-\sqrt{2}}=a^{\sqrt{2}+1-\sqrt{2}}=a\\\\148) (a^{\sqrt{3}})^{\sqrt{3}}$=a^{\sqrt{3}*\sqrt{3}}=a^{3}$