a)  6 9 : 6 7 = 6 9 - 7 = 6 2

b)  7 5 : 7 2 = 7 5 - 2 = 7 3

c)  11 8 : 11 3 : 11 2 = 11 8 - 3 - 2 = 11 3

d)  x 8 - 7 - 1 = x 0 = 1

a)  6 2

b)  7 3

c)  11 3

d)  x 0

a, 6 9 : 6 7 = 6 9 - 7 = 6 2

b,  7 5 : 7 2 = 7 5 - 2 = 7 3

c,  11 8 : 11 3 : 11 2 = 11 8 - 3 - 2 = 11 3

d,  x 8 : x 7 : x = x 8 - 7 - 1 = x 0 = 1

\(a,3^4.3^5=3^{4+5}=3^9\\ b,12^8:12=12^{8-1}=12^7\\ c,4.8^6.2.8^3=\left(4.2\right).\left(8^6.8^3\right)=8.8^{6+3}=8.8^9=8^{1+9}=8^{10}\)

\(a.3^4.3^5=3^9\)

\(b.12^8:12=12^7\)

\(c.4.8^6.2.8^3\)

\(=\left(4.2\right)8^6.8^3\)

\(=8.8^6.8^3=8^{10}\)

243 : 3³ : 3 = 3⁵ : 3³ : 3¹ = 3^{5 - 3 - 1} = 3¹

= 3

\(a,5\cdot p\cdot5\cdot p\cdot2q\cdot4q\)

\(=5^2\cdot p^2\cdot2\cdot q\cdot2^2\cdot q\)

\(=5^2\cdot2^3\cdot p^2\cdot q^2\)

\(b,a\cdot a+b\cdot b+c\cdot c\cdot c+d\cdot d\cdot d\cdot d\)

\(=a^2+b^2+c^3+d^4\)

#Urushi

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. \(y^{50}:\left(y^5\right)^3:\left(y^2\right)^{10}\)

\(=y^{50}:y^{15}:y^{20}\)

\(=y^{50-15-20}\)

\(=y^{15}\)

a)  3.3^4.3^5 = 3^10

b) 7^3 : 7^2 : 7 = 7^0

c) (x^4)^3 = x^12

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) \(9^3\cdot3^2\)

\(=\left(3^2\right)^3\cdot3^2\)

\(=3^6\cdot3^2\)

\(=3^8\)

b) \(x^7\cdot x:x^4\)

\(=x^8:x^4\)

\(=x^4\)

c) \(7\cdot3^9+3^{10}+51\cdot3^8\)

\(=3^8\cdot\left(7\cdot3+3^2+51\right)\)

\(=3^8\cdot81\)

\(=3^8\cdot3^4\)

\(=3^{12}\)

d) \(5^{15}\cdot125^3\cdot625\)

\(=5^{15}\cdot5^9\cdot5^4\)

\(=5^{28}\)