"Powers to powers and products to powers" PPT courseware

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"Powers to powers and products to powers" PPT courseware

Part One: Classroom Thoughts

1. If a2n=5, find a6n

2. If am=2, a2n=7, find a3m+4n

3 Compare the sizes of 2100 and 375.

4 Given that 44×83=2x, find the value of X.

Knowledge review

fill in the blank:

1. am+am=_____, based on ______________.

2. a3·a5=____, based on ____________________.

3. If am=8, an=30, then am+n=____.

4. (a4)3=_____, based on ____________________.

5. (m4)2+m5·m3=____, (a3)5·(a2)2=____.

Part 2: Properties of Operations

Operational properties of products raised as powers:

(ab)n=_____. (n is a positive integer)

To raise the power of a product, multiply each factor of the product, and then multiply the resulting powers together.

Example 1 Calculation:

(1)(5m)3 (2)(-xy2)3 (3)(3×103)2

Example 2 Calculation:

(1) (3xy2)2 (2)(-2ab3c2)4

Part Three: Practice

1. Calculate:

(1) (-3x2y)3 (2) (-5ab)2

(3) (2xnym)2 (4) (-2xy2z3)4

2. Calculate:

⑴ (-a2)3.(-a3)2

⑵ -(n2).(-n5)3

⑶ a5.a3+(2a2)4

⑷ (-2a)3－(-a).(a)2

Part 4: Exercises

The inner wall radius r of a cylindrical oil storage tank is 20m, and the height h is 40m.

(1) What is its volume L? (1m3 =103L)

Solution: V =πr²H

≈3.14×(2×10)2×(4×10)

=3.14×(4×102)×(4×10)

=3.14×(42×103)

=5.0×104m3

=5.0×107 (L)

Answer: The volume of the oil storage tank is 5.0×107L.

(2) If the maximum oil storage height of the oil storage tank is 30m, how many liters of oil can it store at most? (1m3 =103L)

Solution: V =πr²h

≈3.14×(2×10)2×(3×10)

=3.14×(4×102)×(3×10)

=3.14×(1.2×104)

=3.8×104m3=3.8×107L

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