Exponents Question
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Grade 9 Exponents CCSS: HSN-RN.A.1
Which of the following is a reason why, when dealing with an equation or expression, one would switch from using radical notation (square roots, cube roots, etc), to rational exponents? Choose all correct answers.
- One can use exponent laws to simplify the expression or equation. For example, 3√x6⋅√x9 becomes x63⋅x92=x2+92=x42+92=x132.
- It avoids the issue of complex numbers. For example, √-2 is complex, namely 2i where i is the square root of -1, but changing this into a rational exponent, -212, it is no longer complex.
- For an expression or equation with division, once the radical has been converted to a rational exponent, the factors can be more easily divided. For example, √8x74√4x3 becomes 8x724x34=2x72-34=2x144-34=2x114.
- Using rational exponents can lead to easier forms for evaluation. For example, 3√46 can be written as 463=42, which can then be easily evaluated.