A) 13^ 5 •13^ 6=13^11 B) (-123)^ 3 • (-123)^ 9=(-123)^12 C) 6^ 11 • 6• 6^ 12 =6^24 D) -17^ 9 / -17 ^ 4=-17^5 E) (1 1/3) ^ 13 : 1 1/3=(1/3)^12 F) 8^ 14 •8^ 16 / 8 ^15=8^30/8^15=8^15 G) a^ 9 • a ^6 / a^ 4 =a^15/a64=a^11 H) x ^11 •x^ 5 •x / x ^18 : x^ 9 =x^16/x^18:x^9=x^-2:x^9=x^-11 I) b^ 7 •b^ 7 : (b^ 2 •b) / b^ 4 • b ^2 :b =b^14: b^3/b^5=b^11/ b^5=b^6
[latex]a) 13^{5}cdot13^{6} = 13^{5+6} = 13^{11}\\b) (-123)^{3}cdot(-123)^{9} = (-123)^{3+9} = (-123)^{12} = 123^{12}\\c) 6^{11}cdot6cdot6^{12} = 6^{11+1+12} = 6^{24}\\d) frac{-17^{9}}{-17^{4}} = -17^{9-4} = -17^{5}\\e) (1frac{1}{3})^{13}:(1frac{1}{3})=(1frac{1}{3})^{13-1} = (1frac{1}{3})^{12}\\f) frac{8^{14}cdot8^{16}}{8^{15}} = 8^{14+16-15} = 8^{15}\\g) frac{a^{9}cdot a^{6}}{a^{4}}=a^{9+6-4} = a^{11}[/latex] [latex]h) frac{x^{11}cdot x^{5}cdot x}{x^{18}: x^{9}}=frac{x^{17}}{x^{9}}=x^{8}\\i) frac{b^{7}cdot b^{7}:(b^{2}cdot b)}{b^{4}cdot b^{2}:b} = frac{b^{14}:b^{3}}{b^{6}:b}=frac{b^{11}}{b^{5}} = b^{6}[/latex]