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

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

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

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

   • 3x²
   • 20.25x²
   • 3x^32
   • 81x²
4. 4.

   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?

   • 65,536
   • 4.75
   • 2
   • 4
5. 5.

   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
   • 4
   • about 0.19
   • 48
6. 6.

   Ren enlarges a square quilt so its area is 9 times the old area. Each side is multiplied by what factor?

   • 4.5
   • 3
   • about 2.1
   • 9
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
   • about 21.3
   • 8
8. 8.

   A rectangular poster is reduced to 1/4 of its area, keeping its shape. Its width was 40 cm. Milo finds the new width. What is it?

   • 20 cm
   • about 25.2 cm
   • 10 cm
   • 5 cm
9. 9.

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

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

    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.
    • 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.
    • 4^(-1/2) is greater: it equals 1/2, and 27^(-1/3) equals 1/3.