Simplify \(\frac{t^{15}}{t^{6}}\).
Question 1 Report
Simplify \(\frac{t^{15}}{t^{6}}\).
Answer Details
When dividing powers of the same base, subtract the indices: \( a^{m} \div a^{n} = a^{m-n} \).
Both terms have base \( t \), so \[ \frac{t^{15}}{t^{6}} = t^{15-6} = t^{9} \] [B1]
The rule follows from what an index means. The numerator is 15 factors of \( t \) multiplied together and the denominator is 6 factors, so 6 of the factors cancel in pairs, leaving \( 15 - 6 = 9 \) factors of \( t \), which is \( t^{9} \).
The usual errors are dividing the indices to get \( t^{2.5} \), or subtracting the wrong way round to get \( t^{-9} \). Subtraction of indices applies only when the bases are identical, as they are here.
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