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1.
a) \(3^4\times3^5\times3^6=3^{4+5+6}=3^{15}\)
b) \(5^2\times5^4\times5^5\times25=5^2\times5^4\times5^5\times5^2=5^{2+4+5+2}=5^{13}\)
c) \(10^8\div10^3=10^{8-3}=10^5\)
d) \(a^7\div a^2=a^{7-2}=a^5\)
2.
\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)
\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)
\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)
a. 2^3 . 2^2 . 2^4
= 2^9
b. 10^2 . 10^3 . 10^5
= 10^10
c. x. x^5
= x^6
d. a^3 . a^2 . a^5
= a^10
a) \(2^3.2^2.2^4\)
\(=2^{3+2+4}\)
\(=2^9\)
b) \(10^2.10^3.10^5\)
\(=10^{2+3+5}\)
\(=10^{10}\)
c) \(x.x^5=x^1.x^5=x^6\)
d) \(a^3.a^2.a^5=a^{3+2+5}=a^{10}\)
2^(10 : 64 x 16) = 2^[(10 x 16) : 64] = 2^(160 : 64) = 2^25
2^(10 x 8) = 2^80 3^(5 : 27) = 3^(5/27) 5^(2 x 125) = 5^250 6^(6 : 36) = 6^(1/6)
a ) 100000 : 10 3 = 10 5 : 10 3 = 10 2 b ) 11 5 : 121 = 11 5 : 11 2 = 11 3 c ) 243 : 3 3 : 3 = 3 5 : 3 3 : 3 = 3 1 d ) 4 8 : 64 : 16 = 4 8 : 4 3 : 4 = 4 4
1) 35 . 45 = (3.4)5 = 125
2) 85 . 23 = 215 . 23 = 218