Identify the greater number in each of the following— (i) 4³ or 3⁴ (ii) 2⁸ or 8² (iii) 100² or 2¹⁰⁰

(i) 3⁴ = 81 is greater than 4³ = 64 (ii) 2⁸ = 256 is greater than 8² = 64 (iii) 2¹⁰⁰ is much greater than 100² = 10000 — (i) 4³ = 4 × 4 × 4 = 64 and 3⁴ = 3 × 3 × 3 × 3 = 81. So 3⁴ > 4³. (ii) 2⁸ = 256 and 8² = 64. So 2⁸ > 8². (iii) 100² = 10000 while 2¹⁰⁰ is approximately 1.27 × 10³⁰, which is astronomically larger.

Identify the greater number in each of the following— (i) 4³ or 3⁴…

Question 8 of 28intermediate🔧 ApplyNumerical3 marks

Identify the greater number in each of the following— (i) $4^3$ or $3^4$
(ii) $2^8$ or $8^2$
(iii) $100^2$ or $2^{100}$

(i)

Answer

$3^4 = 81$ is greater than $4^3 = 64$

(ii)

Answer

$2^8 = 256$ is greater than $8^2 = 64$

(iii)

Answer

$2^{100}$ is much greater than $100^2 = 10000$

Explanation

(i) $4^3 = 4 \times 4 \times 4 = 64$ and $3^4 = 3 \times 3 \times 3 \times 3 = 81$ . So $3^4 > 4^3$ . (ii) $2^8 = 256$ and $8^2 = 64$ . So $2^8 > 8^2$ . (iii) $100^2 = 10000$ while $2^{100}$ is approximately $1.27 \times 10^{30}$ , which is astronomically larger.

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