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2:
a: n=5^4
=>n=625
b: n^3=125
=>n^3=5^3
=>n=5
c: 11^n=1331
=>11^n=11^3
=>n=3
a) \(3\cdot3^4\cdot3^5=3^{10}\)
b) \(7^3:7^2:7=7^{3-2-1}=7^0\)
c) \(\left(x^4\right)^3=x^{12}\)
a) \(4^9:4^4\)
\(=4^{9-4}\)
\(=4^5\)
b) \(17^8:17^5\)
\(=17^{8-5}\)
\(=17^3\)
c) \(2^{10}:8^2\)
\(=2^{10}:\left(2^3\right)^2\)
\(=2^{10-6}\)
\(=2^4\)
d) \(18^{10}:3^{10}\)
\(=\left(18:3\right)^{10}\)
\(=6^{10}\)
e) \(27^5:81^3\)
\(=\left(3^3\right)^5:\left(3^4\right)^3\)
\(=3^{15}:3^{12}\)
\(=3^{15-12}\)
\(=3^3\)
f) \(10^6:100\)
\(=10^6:10^2\)
\(=10^{6-2}\)
\(=10^4\)
g) \(5^9:25^3\)
\(=5^9:\left(5^2\right)^3\)
\(=5^9:5^6\)
\(=5^{9-6}\)
\(=5^3\)
h) \(4^{10}:64^3\)
\(=4^{10}:\left(4^3\right)^3\)
\(=4^{10-9}\)
\(=4\)
i) \(2^{25}:32^4:18^4:9^4\)
\(=\left(2^{25}:2^{20}\right):\left(18^4\cdot9^4\right)\)
\(=2^5:9^8:2^4\)
\(=2:9^8\)
\(=\dfrac{2}{9^8}\)
\(a,3^4.3^5=3^{4+5}=3^9\\ b,12^8:12=12^{8-1}=12^7\\ c,4.8^6.2.8^3=\left(4.2\right).\left(8^6.8^3\right)=8.8^{6+3}=8.8^9=8^{1+9}=8^{10}\)
\(a.3^4.3^5=3^9\)
\(b.12^8:12=12^7\)
\(c.4.8^6.2.8^3\)
\(=\left(4.2\right)8^6.8^3\)
\(=8.8^6.8^3=8^{10}\)
A. \(256:2^5\cdot4\)
\(=2^6:2^5\cdot2^2\)
\(=2^{6-5+2}\)
\(=2^3\)
B. \(\left(4x^2\right)^8:\left(4x^2\right)^4:\left(4x^2\right)^2\)
\(=\left(4x^2\right)^{8-4-2}\)
\(=\left(4x^2\right)^2\)
\(=\left[\left(2x\right)^2\right]^2\)
\(=\left(2x\right)^4\)
C. \(y^{50}:\left(y^5\right)^3:\left(y^2\right)^{10}\)
\(=y^{50}:y^{15}:y^{20}\)
\(=y^{50-15-20}\)
\(=y^{15}\)
`3.5 .15.15 = 3.5.3.5.3.5 = 3^3.5^3`
`2.2.5.2.5 = 2^3 . 5^2`
`1000.10 .10 = 10^3 .10^1 . 10^1 = 10^5`
`a.a.a.b.b.b = a^3 . b^3`
`n.n.n + p.p = n^3 . p^2`
a: =15*15*15=15^3
b: =2^3*5^2
c: =10^3*10^2=10^5
d: =a^3*b^3
e: =n^3+p^2
a: 6*6*6*6*6=6^5
b: 25*25*25*5=5^2*5^2*5^2*5=5^7
c: 8*2*2*16*4
=2^3*2^2*2^4*2^2
=2^11
d: \(3\cdot3\cdot3\cdot15\cdot5\cdot5\cdot5=15\cdot15\cdot15\cdot15=15^4\)
\(4.16^5.32=2^2.2^{20}.2^5=2^{27}\)
\(72^4.81^{10}=2^{12}.3^8.3^{40}=2^{12}.3^{48}=2^{12}.\left(3^4\right)^{12}=2^{12}.81^{12}=243^{12}\)