Q. Write equivalent forms of the following. (i) 2⁻⁴(ii) (ii) 10⁻⁵ (iii) (-7)⁻² ((iv) (-5)⁻³
(v) 10⁻¹⁰⁰
Here are the equivalent forms for each expression:
(i) 2⁻⁴
Using the definition of negative exponents: n⁻ᵃ = 1/nᵃ
2⁻⁴ = 1/2⁴ = 1/16
(ii) 10⁻⁵
Using the same definition:
10⁻⁵ = 1/10⁵ = 1/100,000
(iii) (-7)⁻²
For this case:
(-7)⁻² = 1/(-7)² = 1/49
(iv) (-5)⁻³
(-5)⁻³ = 1/(-5)³ = 1/(-125) = -1/125
(v) 10⁻¹⁰⁰
10⁻¹⁰⁰ = 1/10¹⁰⁰
This last one is a very small decimal number with 1 followed by 100 zeros in the denominator, or written with a decimal point:
0.0000000000...0001 (with 99 zeros after the decimal point before the 1)
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