Simplify and express in exponential form: [(52)3×54]÷57 [3 MARK

Question

Simplify and express in exponential form:

[(5^{2})^{3} \times 5^{4}] \div 5^{7}

[3 MARKS]

Answer:
:
Steps: 2 Marks
Answer: 1 Mark

= [(5^{2})^{3} \times 5^{4}] \div 5^{7}

= [5^{6} \times 5^{4}] \div 5^{7}

[∵ (a^{m})^{n} = a^{m \times n}]

= [5^{6 + 4}] \div 5^{7}

[∵ a^{m} \times a^{n} = a^{m + n}]

= 5^{10} \div 5^{7}

= 5^{10 - 7}

[∵ a^{m} \div a^{n} = a^{m - n}]

= 5^{3}

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