Rational exponents and the laws of exponents

Grade 9 Math Worksheet - Challenge Me

Circle the best answer.

1. 1.

   A town's population multiplies by 81 over 4 years at a steady yearly factor f. Kira wants f. What is it?

   • 20.25
   • 9
   • 21
   • 3
2. 2.

   A video's views multiply by 8 over 3 weeks at a steady weekly factor f. Luz wants f. What is it?

   • 2
   • about 3.33
   • about 2.83
   • about 2.67
3. 3.

   A pond's algae shrinks to 1/27 of its size over 3 days at a steady daily factor f. Zee wants f. What is it?

   • about 0.19
   • about 0.68
   • 1/81
   • 1/3
4. 4.

   An account multiplies by 25 in one year at a steady rate. Jun wants the factor for each half-year. What is it?

   • 13
   • about 2.9
   • 5
   • 12.5
5. 5.

   Pia writes 4^(1/2) × 9^(1/2) = 36^(1/2) = 6, then checks by finding each root first. Is the step right?

   • Yes: 4^(1/2) × 9^(1/2) = 2 × 3 = 6, and 36^(1/2) = 6, so the two roots multiply.
   • No: multiplying powers adds exponents, so 4^(1/2) × 9^(1/2) = 36^1 = 36.
   • No: a half power halves the base, so 4^(1/2) × 9^(1/2) = 2 × 4.5 = 9.
   • No: the bases 4 and 9 differ, so the product cannot be rewritten as one power.
6. 6.

   Milo writes (-4)^(1/2) = -2, because the square root of 4 is 2 and the minus sign comes along. Which response is correct?

   • Yes: the square root of 4 is 2, and the minus sign stays, so it is -2.
   • No: the minus sign drops under a root, so (-4)^(1/2) = 2.
   • No: (-2)² = 4, not -4, and no real number squares to -4.
   • Yes: (-2) × (-2) = -4, so -2 squared is -4.
7. 7.

   Ren solves (x - 2)^(1/2) = 6 for x. What is x?

   • 36
   • 38
   • 34
   • about 4.4
8. 8.

   Bo solves (x + 5)^(1/3) = 2 for x. What is x?

   • 3
   • -1
   • 8
   • 13
9. 9.

   Esme solves (x + 3)^(1/2) = 5 for x. What is x?

   • 28
   • 7
   • 22
   • 25
10. 10.

    Zee solves 2 × x^(1/3) = 8 for x. What is x?

    • 4
    • 64
    • 512
    • 16