Choose the correct word/answer and fill in the blanks :
${(2^{3})}^{2} \div 2^{3} =________(2^{6 - 3} / 2^{9 - 3})$

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Solution

By the properties of exponent, we know that -
${(a^{x})}^{y} = a^{x \times y} a^{x} \div a^{y} = a^{x - y}$
By using the above properties -
${(2^{3})}^{2} \div 2^{3} = 2^{3 \times 2} \div 2^{3} = 2^{6} \div 2^{3} = 2^{6 - 3}$
Hence, the correct answer is $2^{6 - 3}$ .

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