2^5.2^4:2^2.1/16=(2^7)/16

\(\frac{32\cdot2^4}{2^2\cdot\frac{1}{16}}\)

\(=\frac{2^5\cdot2^4}{\frac{4}{16}}\)

\(=\frac{2^9}{\frac{1}{4}}\)

\(=2^9\cdot4\)

\(=2^9\cdot2^2\)

\(=2^{11}\)

    32 . 2⁴ : ( 2² . 1/16 ) 

=  2⁵ . 2⁴ : 1/2²

=  2⁹ . 2²

= 2¹¹

\(\frac{2^7}{16}\)

1) a) 4⁸.2²⁰ = (2²)⁸.2²⁰

= 2¹⁶.2²⁰ = 2³⁶

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9¹².27⁵.81³ = (3²)¹².(3³)⁵.(3⁴)⁴

= 3²⁴.3¹⁵.3¹⁶ = 3⁵⁵

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64³.4⁵.16² = (4³)³.4⁵.(4²)²

= 4⁹.4⁵.4⁴ = 4¹⁸

b) 25²⁰.125⁴ = (5²)²⁰.(5³)⁴

= 5⁴⁰.5¹² = 5⁵²

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x⁷.x³.x⁴ = x¹⁴

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3⁶.4⁶ = (3.4)⁶ = 12⁶

2) a) 2² = 4

2³ = 8

2⁴ = 16

2⁵ = 32

2⁶ = 64

2⁷ = 128

2⁸ = 256

2⁹ = 512

2¹⁰ = 1024

b) 3² = 9

3³ = 27

3⁴ = 81

3⁵ = 243

c) 4² = 16

4³ = 64

4⁴ = 256

d) 5² = 25

5³ = 125

5⁴ = 625

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: \(25^4\cdot2^8=100^4\)

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

c) \(\left(\dfrac{5}{4}\right)^4:\left(\dfrac{15}{2}\right)^4=\left(\dfrac{5}{4}:\dfrac{15}{2}\right)^4=\left(\dfrac{1}{6}\right)^4\)

d) \(10^4:16=10^4:2^4=\left(10:2\right)^4=5^4\)

e) \(\left(-2\right)^3.125=\left(-2\right)^3.5^3=\left(-2.5\right)^3=-10^3\)

f) \(64^3:\left(-2\right)^9=64^3:\left(-8\right)^3=\left(64:-8\right)^3=-8^3\)

\(=\left(-2\right)^6.5^3\)

a)(-8).(-2)^3.125=(-2)^3.(-2)^3.5^3=1^3=1

a: \(1=4^0\)

\(4=4^1\)

\(16=4^2\)

\(256=4^4\)

b: \(\dfrac{1}{4}=4^{-1}\)

\(\dfrac{1}{64}=4^{-3}\)

\(\dfrac{1}{256}=4^{-4}\)

\(\dfrac{1}{16}=4^{-2}\)

\(\dfrac{1}{1024}=4^{-5}\)