Chapter 8: Exponents and Powers

Ans: False.

RHS = (ab)pq

Using law of exponents, am × an = am+n

Therefore, (ab)pq = (a)pq x (b)pq

L H S ≠ R H S

Ans: True

${\text{RHS  = }}{\left( {\dfrac{y}{x}} \right)^{ - m}} = {\left( {\dfrac{x}{y}} \right)^m} = \dfrac{{{x^m}}}{{{y^m}}} = {\text{LHS}}$

Ans: True

Using law of exponents, ${x^{ - m}} = \dfrac{1}{{{x^m}}}$

${a^m} = \dfrac{1}{{{a^{ - m}}}}$

Ans: True

${\left( { - 2} \right)^4} \times {\left( {\dfrac{5}{2}} \right)^4} = {\left( 2 \right)^4} \times {\left( {\dfrac{5}{2}} \right)^4}$

= ${2^4} \times \dfrac{{{5^4}}}{{{2^4}}} = {5^4}$

Ans: True
For standard form, 0.000037 = 0.37 x 10-4= 3.7 x 10-5

Ans: True
For standard form, 203000 = 203 x 10 x 10 x 10 = 203 x 103
= 2.03 x 102 x 103= 2.03 x 105

Ans: False

As, $2 \times {10^{ - 2}} = 2 \times \dfrac{1}{{{{10}^2}}} = 2 \times \dfrac{1}{{100}} = 0.02$

Ans: False

As, ${5^{ - 2}} = \dfrac{1}{{{5^2}}} = \dfrac{1}{{25}} \ne 25$

Ans: True
e.g. 2350000 = 235 x 10 x 10 x 10 x 10 = 235 x 104
= 2.35 x 104 x 102 =2.35 x 106

Ans: True

LHS = am × bm = (a × b)m = (ab)m