Rational exponents and the laws of exponents
Grade 9 Math Worksheet
Circle the best answer.
Kira writes (x^6)^(1/2) as one power of x, for x > 0. Which is it?
- x³
- x^(1/6)
- x^(13/2)
- x^12
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?
- 50
- 40
- 5
- 10
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
- 2
- 4.75
- 4
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
- 48
- about 0.19
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
- 8
- 64
- about 21.3
Tala's cube-shaped planter has edge 30 cm. A bigger similar cube holds 8 times as much soil. What is the new edge?
- about 84.9 cm
- 60 cm
- 80 cm
- 240 cm
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?
- 5 cm
- about 25.2 cm
- 10 cm
- 20 cm
Pia's robot screen shows 25^(-1/2), a power with a minus sign. What is its value?
- -5
- 5
- 1/5
- 2/25
Noah compares 4^(-1/2) and 27^(-1/3). Which statement is correct?
- 4^(-1/2) is greater: it equals -2, and 27^(-1/3) equals -3.
- 27^(-1/3) is greater, because 27 is a larger base than 4.
- 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.
Esme compares 9^(-1/2) and 125^(-1/3). Which statement is correct?
- 125^(-1/3) is greater: it equals 5, and 9^(-1/2) equals 3.
- 9^(-1/2) is greater: it equals -3, and 125^(-1/3) equals -5.
- 9^(-1/2) is greater: it equals 1/3, and 125^(-1/3) equals 1/5.
- 125^(-1/3) is greater, because 125 is a larger base than 9.