Rational exponents and the laws of exponents

Grade 9 Math Worksheet

Circle the best answer.

1. 1.

   Ari writes (x^12)^(1/3) as one power of x, for x > 0. Which is it?

   • x^(37/3)
   • x^(1/12)
   • x⁴
   • x^36
2. 2.

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

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

   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?

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

   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?

   • 10
   • 50
   • 40
   • 5
5. 5.

   Bacteria multiply by 16 every day at a steady rate. Noah wants the factor for one quarter of a day. By what factor do they multiply?

   • 4.75
   • 65,536
   • 2
   • 4
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?

   • 68
   • 48
   • 4
   • about 0.19
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?

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

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

   • 4
   • 3/64
   • 1/4
   • -4
9. 9.

   Noah compares 4^(-1/2) and 27^(-1/3). Which statement is correct?

   • 27^(-1/3) is greater: it equals 3, and 4^(-1/2) equals 2.
   • 4^(-1/2) is greater: it equals 1/2, and 27^(-1/3) equals 1/3.
   • 27^(-1/3) is greater, because 27 is a larger base than 4.
   • 4^(-1/2) is greater: it equals -2, and 27^(-1/3) equals -3.
10. 10.

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

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