To keep loyal customers happy, a phone tariff's data-rollover calculator uses the expression \(\left(3a^2\right)^3 \div a^4\), where \(a\) is a scaling fact...
Question 1 Report
To keep loyal customers happy, a phone tariff's data-rollover calculator uses the expression \(\left(3a^2\right)^3 \div a^4\), where \(a\) is a scaling factor applied each billing cycle, to work out how much unused data a customer is allowed to carry forward into the next month.
Simplify \(\left(3a^2\right)^3 \div a^4\) fully. (2)
Answer Details
A power raised to another power multiplies the indices and applies to every factor inside the brackets, including any numerical coefficient; dividing powers of the same base then subtracts the indices.
\((3a^2)^3=3^3\times a^{2\times3}=27a^6\) [1 mark]
\(27a^6\div a^4=27a^{6-4}=27a^2\) [1 mark]
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