Flynn Lambert
12/21/2023 · Primary School
Write equivalent expressions for \( \mathrm{x}^{7} \cdot \mathrm{x}^{-2} \) and \( \frac{\mathrm{x}^{7}}{\mathrm{x}} \). What do you notice? Explain how your results relate to the properties of integer exponents.
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The equivalent expressions are \( \mathrm{x}^{7} \cdot \mathrm{x}^{-2} = \mathrm{x}^{5} \) and \( \frac{\mathrm{x}^{7}}{\mathrm{x}} = \mathrm{x}^{6} \). The results show how multiplying by a negative exponent subtracts from the exponent and how dividing by a base with an exponent also subtracts from the exponent, illustrating the properties of integer exponents.
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