Which of the following equals $4^{3} - 3^{3}$ ?

6^{2} + 1

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6^{2} - 1

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57

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62

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Solution

The correct option is A $6^{2} + 1$
For the base of 4 and exponent of 3, the value of base is multiplied exponents times.
Hence, 4(base) is multipled 3(exponent) times.
$4^{3} = 4 \times 4 \times 4 = 64$
Hence, $4^{3} = 4 \times 4 \times 4 = 64$

Similiarly,
$3^{3} = 3 \times 3 \times 3 = 27 \Rightarrow 4^{3} - 3^{3} = 64 - 27 = 37$

$∵ 6^{2} = 36 \Rightarrow 37 = 36 + 1 = 6^{2} + 1$

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