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Power Rules

• When raising a power to a power, multiply the exponents.
• When raising a product to a power, raise each factor to the power.
• The difference between multiplying two powers and raising a power to a power occurs with the exponents. In multiplying two powers you add the exponents. When raising a power to a power you multiply the exponents.

• 42 ×2 =
• 44 =

• 53 ×( − 2) =

(9 − 4) − 7 =

• 9 − 4 ×( − 7) =

• 43 ×x3 =

(xy2) − 4 =

• x − 4 ×y2 ×( − 4) =

([1/2]a2b − 5)2 =

• [1/4] ×a2 ×2 ×b − 5 ×2 =

Use the formula Surface Area = 4π r2 to find the surface area of a sphere with radius 5 × 10−3 m . Use π = 3.14.

• SA = (4)(3.14)(5 ×10 − 3 m)2 =
• (12.56)(25 ×10 − 6 m2) =

Compare the two values: 35 ·3 − 2 and (35)−2.

• 35 ·3−2 = 35 − 2 = 33

Find the area of a square whose sides are 3.2 ×104 inches.

• A = s2
• A = (3.2 ×104 in)2 =

Find the volume of a sphere with a radius of 8.1 ×10 − 2 inches. Use the formula Volume = [4/3]πr3 and leave your answer in terms of π .

• V = [4/3]π(8.1 ×10−2 in)3
• V = [4/3]π(531.441 ×10 − 6 in3)

V = 708.588π×10 − 6 in3

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.