Exponents play a major part in number sense tests, and we have had many lessons which included them. Today we will work on exponents with fractions in them. This concept appeared 4 times last year, with a median placement at question # 78.
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Number Dojo Level: 308
To understand exponents with fractions, we need to understand both powers and roots. In any fractional exponent:
- the numerator represents the power, and
- the denominator represents the root.
- cubing it (or taking it to the 3rd power), and
- taking the square root...though not necessarily in that order.
Just like I have a rule that says "divide before you multiply," I prefer to "take the root before the power." This ensures I am working with smaller numbers, which are easier to manipulate and calculate than larger ones.