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b: \(3^4\cdot3^5:\dfrac{1}{27}==3^9\cdot3^3=3^{12}\)
a: \(2^6\cdot3^3=\left(2^2\cdot3\right)^3=12^3\)
b: \(6^4\cdot8^3=2^4\cdot3^4\cdot2^9=2^{13}\cdot3^4\)
c: \(16\cdot81=36^2\)
d: \(25^4\cdot2^8=100^4\)
a) 53 . 52 . 5
= 55 . 5
= 55 . 51
= 56
b) 69 : 64
= 65
c) 4 . 8 . 16 . 32
= 22 . 23 . 24 . 25
= 25 . 24 . 25
= 29 . 25
= 214
a) \(\dfrac{9}{4}-3y+y^2\)
\(=\left(\dfrac{3}{2}\right)^2-3y+y^2\)
\(=y^2-2\cdot\dfrac{3}{2}\cdot y+\left(\dfrac{3}{2}\right)^2\)
\(=\left(y-\dfrac{3}{2}\right)^2\)
b) \(x^3+6x^2y+12xy^2+8y^3\)
\(=x^3+6x^2y+12xy^2+\left(2y\right)^3\)
\(=x^3+3\cdot x^2\cdot2y+3\cdot x\cdot\left(2y\right)^2+\left(2y\right)^3\)
\(=\left(x+2y\right)^2\)
a: \(\left(\dfrac{1}{5}\right)\cdot\left(\dfrac{1}{5}\right)^{15}=\left(\dfrac{1}{5}\right)^{1+15}=\left(\dfrac{1}{5}\right)^{16}\)
b: \(\left(-10,2\right)^{10}:\left(-10,2\right)^3=\left(-10,2\right)^{10-3}=\left(-10,2\right)^7\)
c: \(\left[\left(-\dfrac{7}{9}\right)^7\right]^8=\left(-\dfrac{7}{9}\right)^{7\cdot8}=\left(-\dfrac{7}{9}\right)^{56}\)
6:=(3/2)*(3/2)^2*(3/2)^4=(3/2)^7
7: =(1/2)^7*2^3*2^5*2^8=2^9
8: =(-1/7)^4*5^4=(-5/7)^4
9: =2^2*2^5:(2^3/2^4)
=2^7/2=2^6
10: =(1/7)^3*7^2=1/7
