Question

Identify the greater number, wherever possible, in each of the following?

1. $4 ^3$ or $3^4$
2. $5 ^3$ or $3^5$
3. $2 ^8$ or $8^2$
4. $100^2$ or $2^{100}$
5. $2 ^{10}$ or $10^{2}$

Answer 1

(i) $4^3 = 4 \times 4 \times 4 = 64$
$3^ 4 = 3 \times 3 \times 3 \times 3 = 81$
Therefore, $34 > 43$

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(ii) $5^3 = 5 \times 5 \times 5 =125$
$3^ 5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$
Therefore, $35 > 53$

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(iii) $2^8 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 256$
$8^ 2 = 8 \times 8 = 64$
Therefore, $28 > 82$

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(iv) $100^2$ or $2^{100}$
$2^{ 10 }= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 1024$
$2^{ 100}$ = $1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024$
$100^2 = 100 \times 100 = 10000$
Therefore, $2^{100} > 100^2$

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(v) $2^{10}$ and $10^2$
$2^{ 10 }= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 1024$
$10^2 = 10 \times 10 = 100$
Therefore, $2^{10} > 10^2$