If \(x^2 \times x^3 = x^a\) and \(\frac{x^2}{x^b} = x^1\), what is the value of \(a + b\)?
6
Using the law of indices \(x^m \times x^n = x^{m+n}\): \(x^2 \times x^3 = x^{2+3} = x^5\), so \(a = 5\).
Using \(\frac{x^m}{x^n} = x^{m-n}\): \(\frac{x^2}{x^b} = x^{2-b} = x^1\), so \(2 - b = 1\), giving \(b = 1\).
Therefore \(a + b = 5 + 1 = 6\).
Hence, the value of \(a + b\) is 6.
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