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Mastering Rational Number Exponents
1. TEACHING TIME: 20NN, N, N.
PEOPLE'S EDUCATION PRESS, THE FIRST VOLUME OF MATHEMATICS CLASS
POWER OF RATIONAL
NUMBER
2. learning target
1. Understand and master the concepts and meanings of powers, bases and exponents of rational
numbers. (emphasis)
2. Be able to perform the power operation of rational numbers correctly. (Difficulties)
3. learning target
Handmade Lamian Noodles is a traditional pasta in China. When making, Master Lamian Noodles
kneaded a ball of good noodles into a long strip, then stretched the two ends in his hand, then folded
the strip in half, stretched it again, and folded it again. Each folding is called a button, and after
repeated operations, it became many thin noodles after six or seven consecutive buckles. If the
buttons were pulled 10 times, can you figure out how many noodles there are?
4. learning target
Question: How many noodles can you make after kneading for 10 times? Please use the formula.
2×2×2×2×2×2×2×2×2×2
Thinking: How many noodles can you make after kneading 100 times? Please use the formula. How
many 2' s are multiplied in the formula?
Think about it: there are 100 2' s in this product. Is there a simple notation for such a long formula?
5. learning target
Generally, n identical factors A are multiplied, which are recorded as an and read as "the nth power
of a (or the nth power of a)", that is, (as shown in the figure)
This operation of finding the product of n identical factors is called power, and the result of power is
called power.
power exponent
The base number can be omitted once without writing, the second power is also called square, and
the third power is also called cubic)
a
X
a
X
a
X a
n
=
......
n个
6. Write the following forms in the form of power, and point out the meaning of base and exponent.
（1）(-2)×(-2)×(-2)；
7. Write the following forms in the form of power, and point out the meaning of base and exponent.
（1）(-2)×(-2)×(-2)；
（2）2/3× 2/3×2/3×2/3
Determine the base first, and then write it in the form of power.
8. Write the following forms in the form of power, and point out the meaning of base and exponent.
（2）2/3× 2/3×2/3×2/3
Determine the base first, and then write it in the form of power.
9. Solution:
(1)(-2)×(-2)×(-2)＝
Base-2 indicates the same factor; The index indicates the number of the same factors.
(2)2/3× 2/3×2/3×2/3 =
The base 2/3 represents the same factor, and the index 4 represents the number of the same factors.
When the base number is negative or a fraction, be sure to enclose the base number in brackets
when writing.
10. Can you quickly judge whether the following powers are
positive or negative?
16
5
0.01
2
(-7)
9
12. law
(1) Any power of 1 is 1;
(2) The power of-1 is very regular:
The odd power of -1 is -1, and the even power of-1 is 1.
Note: When the base number is negative or a fraction, the base number must be bracketed, which is
also the method to identify the base number.
13. 1. The characteristic that the base is a power of 10:
Several powers of 10, there are several zeros after 1.
2. Symbolic rule of rational number power operation:
Any power of a positive number is positive;
The even power of negative number is positive, and the odd power is negative.
3. The same even powers which are opposite numbers are equal, and the same odd powers are
opposite numbers.
14. If | x-3 |+(y+2) 2 = 0, find the value of yx.
Solution: ∵| x-3 | ≥ 0, (y+2)2≥0
And | x-3 |+(y+2) 2 = 0.
∴ |x－3| ＝0，(y+2)2＝0,
∴x＝3,y＝-2,
∴yx＝(－2)3＝－8.
15. TEACHING TIME: 20NN, N, N.
PEOPLE'S EDUCATION PRESS, THE FIRST VOLUME OF MATHEMATICS CLASS
POWER OF RATIONAL
NUMBER
