Properties of Exponents 4

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make an equation where the product’s exponent has the greatest possible value.


How do you know when to multiply, divide, subtract, or add the exponents’ value?


There are many possible answers that make the product’s exponent equal to 9 including:
(x^3)^5 · x^(1/6) = x^9

Source: Robert Kaplinsky

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Imaginary Solutions to a Quadratic Equation

Directions: Using the digits 1 to 9 at most one time each, place a digit …


  1. x^15 . x^(1/6) is not equal to x^9 you have to add the exponent which leaves you with an exponent of 15 1/6

    • I agree Heidi. If the original problem said using from -9 to 9, then a person can use -6/1 rather than 1/6 (which are not the same). This would result in an answer of x^9, assuming everything else remained the same respectively.

      • If you keep it from the digits 1 to 9 a maximum of once each, you could say (x^5)^1 * x^(8/2) = x^9 or (x^1)^5 * x^(8/2) = x^9. There are some other possibilities that will result in x^9. I can think of 4 more that will also result in x^9 with the original restrictions, so a great way to increase the rigor, develop conceptual understanding, and assess numeracy skills would be to identify as many solutions as possible that result in a product with the greatest exponent.

  2. The answer key is definitely wrong!

    My tutoree student found a solution to end up with 9 though!

    (x^1)^5 x^(8/2)= x^9

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