A textbook exercise on index laws, set as revision before a test on Friday morning, asks students to combine two powers of the same base without using a cal...
Question 1 Report
A textbook exercise on index laws, set as revision before a test on Friday morning, asks students to combine two powers of the same base without using a calculator, writing out every factor, or making an error with the signs. Simplify \(k^{7} \times k^{-3}\), giving your answer as a single power of \(k\). (2)
Answer Details
When multiplying powers of the same base, the index law \(a^m \times a^n = a^{m+n}\) applies: the indices are added together, and the base stays the same.
Applying the law with base \(k\) and indices \(7\) and \(-3\), the indices are added: \[7 + (-3) = 4\] [1 mark]
So the simplified single power is \[k^{7} \times k^{-3} = k^{4}\] [1 mark]
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