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

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

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

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

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

#Urushi

\(x^8:x^7:x=x^1:x=1^1\)

x⁸:x⁷:x=x^8-7-1=x⁰=1

x⁸ : x⁷ 

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

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

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

\(c.4.8^6.2.8^3\)

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

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

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

a, 243 : 3³ : 3= 3⁵ : 3³ : 3 = 3^5-3-1 = 3

hoctot

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)  3.3^4.3^5 = 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,  8 2 . 32 4 =  2 3 2 . 2 5 4 = 2 3 . 2 . 2 5 . 4 = 2 6 . 2 20 = 2 6 + 20 = 2 26

b,  27 4 . 9 3 . 243 =  3 3 4 . 3 2 3 . 3 5 =  3 3 . 4 . 3 2 . 3 . 3 5 = 3 12 . 3 6 . 3 5 =  3 12 + 6 + 5 = 3 23

c,  13 2 - 12 2 = 169  - 144 = 25 =  5 2

d,  6 2 + 8 2 = 36 + 64 = 100 =  10 2

e,  5 3 + 5 4 + 125 2 . 5 3 =  5 3 + 5 4 + 5 3 . 2 . 5 3 =  5 3 + 5 4 + 5 6 . 5 3 =  5 3 . 1 + 5 + 5 3 . 5 3 = 5 6 . 131

f,  1 3 + 2 3 + 3 3 + 4 3 + 5 3 = 1 + 8 + 27 + 64 + 125 = 225 =  15 2

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

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

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

\(=y^{15}\)