Rational exponents and the laws of exponents

Grade 9 Math Worksheet

Circle the best answer.

1. 1.

   Kira writes (x^6)^(1/2) as one power of x, for x > 0. Which is it?

   • x^12
   • x^(13/2)
   • x^(1/6)
   • x³
2. 2.

   Esme writes (81x^8)^(1/4) in simplest form, for x > 0. Which is it?

   • 3x²
   • 3x^32
   • 81x²
   • 20.25x²
3. 3.

   Tala writes (27x^9)^(1/3) in simplest form, for x > 0. Which is it?

   • 3x³
   • 27x³
   • 3x^27
   • 9x³
4. 4.

   A yeast culture grows 9-fold every hour: N = 50 × 9^t, with t in hours. Luz finds N at t = 1/2, thirty minutes. What is N?

   • 4,050
   • 150
   • 250
   • 225
5. 5.

   A medicine's amount drops to 1/4 each hour: A = 80 × (1/4)^t, with t in hours. Pia finds A at t = 1/2. How many mg remain?

   • 40
   • 10
   • 50
   • 5
6. 6.

   A sample keeps 1/8 of its mass each week: M = 96 × (1/8)^w, with w in weeks. Zee finds M at w = 1/3. How many grams remain?

   • 4
   • 68
   • about 0.19
   • 48
7. 7.

   A cube-shaped box's volume becomes 64 times as big. Bo wants the factor for each edge. By what factor is each edge multiplied?

   • 8
   • 64
   • about 21.3
   • 4
8. 8.

   Pia's robot screen shows 25^(-1/2), a power with a minus sign. What is its value?

   • 2/25
   • 5
   • 1/5
   • -5
9. 9.

   Ari's lock code is 64^(-1/3), a power with a minus sign. What is its value?

   • 4
   • 1/4
   • 3/64
   • -4
10. 10.

    Esme compares 9^(-1/2) and 125^(-1/3). Which statement is correct?

    • 9^(-1/2) is greater: it equals -3, and 125^(-1/3) equals -5.
    • 125^(-1/3) is greater, because 125 is a larger base than 9.
    • 9^(-1/2) is greater: it equals 1/3, and 125^(-1/3) equals 1/5.
    • 125^(-1/3) is greater: it equals 5, and 9^(-1/2) equals 3.