Exercise 11.2

(i)

(i) 210×24

Answer:

Let's use the law of exponents for multiplication:210×24 = ⁽¹⁰⁺⁴⁾

210+4= 2

(ii)

(ii) 32×324

Answer:

First, let's simplify 324:324=3^(×)

32×4=3

Now, multiply by 32:32×38= 3⁽⁺⁾

32+8=3

(iii)

(iii) 5752

Answer:

Let's use the law of exponents for division:5752=5^-

57−2=5

(iv)

(iv) 92×918×910

Answer:

Let's use the law of exponents for multiplication: 92×918×910 = 9⁽⁺⁺⁾

92+18+10=9

(v)

(v) 354×353×358

Answer:

Let's use the law of exponents for multiplication: 354×353×358 = (3/5)⁽⁺⁺⁾

354+3+8= (3/5)

(vi)

(vi) −33×−310×−37

Answer:

Let's use the law of exponents for multiplication: −33×−310×−37= (-3)⁽⁺⁺⁾

−33+10+7= (−3)

(vii)

(vii) 322

Answer:

Let's use the law of exponents for powers: 322= 3^(×)

32×2= 3

(viii)

(viii) 24×34

Answer:

Let's use the law of exponents for same exponents: 24×34=2×34

2×34= 6

(ix)

(ix) 24a×25a

Answer:

Let's use the law of exponents for multiplication: 24a×25a= 2⁽⁺⁾

24a+5a= 2

(x)

(x) 1023

Answer:

Let's use the law of exponents for powers: 1023 = 10^(×)

102×3= 10

(xi)

(xi) −5625

Answer:

Let's use the law of exponents for powers: −5625= (-5/6)^(×)

−562×5= (−5/6)

(xii)

(xii) 23a+7×27a+3

Answer:

Let's use the law of exponents for multiplication: 23a+7×27a+3= 2^(a++a+)

23a+7+7a+3= 2^{a +}

(xiii)

(xiii) 235

Answer:

Let's write the numerator and denominator with exponents: 235 = 2 / 3

25= and 35=

235=32243

(xiv)

(xiv) −33×−53

Answer:

Let's use the law of exponents for multiplication: −33×−53= [(-3) × (-5)]

−3×−5=

153 =

(xv)

(xv) −46−43

Answer:

Let's use the law of exponents for division: −46−43 = (-4)^(-)

−46−3 = (-4) =

(xvi)

(xvi) 97915

Answer:

Let's use the law of exponents for division: 97915= 9^{( - )}

97−15 = 9

(xvii)

(xvii) −65−69

Answer:

Let's use the law of exponents for division: −65−69= (-6)^{( - )}

−65−9 = (-6)

(xviii)

(xviii) −77×−78

Answer:

Let's use the law of exponents for multiplication: −77×−78 = (-7)^{( + )}

−77+8 = (-7)

(xix)

(xix) −644

Answer:

Let's use the law of exponents for powers: −644= (-6)^(×)

`(-6)^(4×4) = (-6)

(xx)

(xx) ax×ay×az

Answer:

Let's use the law of exponents for multiplication: ax×ay×az= a^{( + + )}

ax+y+z

(i)

(i) 100×1011=1013

100×1011 = 102×1011 = 102+11 = 10

Therefore, the statement is True False

(ii)

(ii) 32×43=125

Left side: 32×43 = 9×64 =

Right side: 125 =

Since 576 ≠ 248832, the statement is False True

(iii)

(iii) 50=1000000

Any non-zero number raised to power 0 equals

50 =

1000000 =

Therefore, the statement is True False

(iv)

(iv) 43=82

43 =

82 =

Therefore, the statement is TrueFalse

(v)

(v) 23>32

23 =

32 =

Since 8 < 9, the statement is False True

(vi)

(vi) −24>−34

−24 =

−34 =

Since 16 < 81, the statement is False True

(vii)

(vii) −25>−35

−25 =

−35 =

Since -32 > -243, the statement is True False