Działania na potęgach

[gosia979]

zad 12 oblicz
a) \(\frac{(1024-2^7)*343}{(2^7*7^5 )}\)=

b) \(\frac{(9\cdot 5^{12}-5^{13})\cdot 8^3}{(2^9 \cdot 625^3 )}\)=

c)\(\frac{8*3^4*3^{11}-9*3^{12}}{46*(3^{18}:3^4 )}\)=

Zad 10 oblicz kozystajac ze wzorow skroconego mnożenia
a)\(97 ^2\) c) \(199*201\)
d)\(64 ^4-36^2\) b)\(81^2\)

[ewelawwy]

12a)
\(\frac{(1024-2^7)\cdot 343}{(2^7\cdot 7^5 )}=\frac{(2^{10}-2^7)\cdot 7^3}{2^7\cdot 7^5}=\frac{2^7(2^3-1)}{2^7\cdot 7^2}=\frac{8-1}{49}=\frac{1}{7}=7^{-1}\)

[ewelawwy]

12c)
\(\frac{8*3^4*3^{11}-9*3^{12}}{46*(3^{18}:3^4 )}=\frac{8\cdot 3^{15}-3^{14}}{46\cdot 3^{14}}=\frac{3^{14}(24-1)}{3^{14}\cdot 46}=\frac{23}{46}=\frac 12\)

[ewelawwy]

10
c) \(199\cdot 201 = (200-1)(200+1)=40000-1=39999\)

[ewelawwy]

10b)
\(81^2=(80+1)^2=6400+160+1=6561\)

[anka]

12 b)
\(\frac{(9\cdot 5^{12}-5^{13})\cdot 8^3}{2^9 \cdot 625^3 } =\frac{15^{12} \cdot (9-5)\cdot 8^3}{2^9 \cdot 5^{12 }}=\frac{15^{12} \cdot 4\cdot 2^9}{2^9 \cdot 5^{12 }}=4\)

[anka]

10.
a)\(97 ^2=(100-3)^2=100^2-2 \cdot 100 \cdot 3+3^2=...\)

[anka]

10.
d)\(64 ^4-36^2=(64^2-36) \cdot (64^2+36)=(64^2-6^2) \cdot (64^2+36)=(64-6) \cdot (64+6) \cdot (64^2+36) =...\)