Simplify \(x^5\times x^3\).
Question 1 Report
Simplify \(x^5\times x^3\).
Answer Details
When powers of the same base are multiplied, the indices are added: \(a^m \times a^n = a^{m+n}\).
Applying this with base \(x\): \[ x^5 \times x^3 = x^{5+3} = x^8 \] [B1]
The rule comes from counting factors. Writing the powers out in full, \(x^5\) is five \(x\) terms multiplied together and \(x^3\) is three more, so altogether there are \(5 + 3 = 8\) factors of \(x\), which is \(x^8\).
The usual error is to multiply the indices and write \(x^{15}\). Multiplying indices belongs to a different rule, raising a power to a power, as in \((x^5)^3 = x^{15}\). Adding is for multiplication of powers, multiplying is for a power of a power, and both rules require the bases to be identical.
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