What is a power of the same base? How do you calculate the power of the same base?

The power of the same base means that the base number is the same.

Multiply (divide) by the power of the same base, the base does not change, and the exponent is added (minus):

a^m×a^n=a^(m+n)

a^m÷a^n=a^(m-n)

a^m=a*a*a...a (m a multiplication).

a^0=1(a≠0)

a)^0=1(a≠0)

A power of the same base is the power of several bases of the same number. Such as:

a, a 2, a 3, a m, a n, they are all powers of the same base.

Hello, the concept of base is relative to the exponent, the index is the number on the shoulder, and the base is the number below.

Multiply by the power of the base, the base does not change, and the exponents are added. For example, 3 and 3 to the fourth power.

Here, 3 is the base, 2 is the exponent, and the power of the same base is multiplied by two numbers that are both 3, and the exponent becomes 2

There is no formula for adding and subtracting to the power of the same base, only terms of the same kind can be added or subtracted.

Multiply by the power of the base, the base does not change, and the exponents are added.

a^m·a^n=a^(m+n)

For example, a 5·a 2 = a (5+2) = a 7

Divide by the power of the same base, the base does not change, and the exponent is subtracted:

a^m÷a^n=a^(m-n)

e.g. a 5 a 2 = a (5-2) = a 3

Note: A m is the m power of a, a n is the n power of a, and a (m+n) is the m+n of a

power. a (m-n) is a m-n power of a.

1. Multiplication of powers of the same base:

a · a · a · a = a m, n, p are all positive integers).

2. Power of power (a) a( Power of product (ab) = a b

3. Division of the same base to the power of the same base:

1) Division to the power of the same base: a a = a( a≠0, m, n are positive integers, and m>n).

2) Zero index: a =1 (a≠0);

3) Exponential power of negative integers: a = a≠0, p is a positive integer), when a = 0 is meaningless, 0 and 0 are meaningless.

A: The same base powers are the same powers of the bases. There are 5 properties between the same base powers, which are applicable to both positive exponential powers and negative exponential powers.

1. Definition: If the base of multiple powers is the same, they are said to be the same base powers.

2. Power calculation.

1.Multiplication. (1) Multiply with the power of the base, the base does not change, and the exponents are added: a m a n=a (m+n)) (m and n are integers).

For example, a 5·a 2 = a (5+2) = a 7

For example, the negative quadratic of a multiplied by the negative cubic of a is equal to the negative fifth power of a.

The power of a multiplied by the power of a is equal to the power of a.

If it is not the same base, it should be changed to the same base first, pay attention to the symbol).

2) 1. The power of the same base refers to the power of the same base.

For example, (-2) is the power of the fifth and (-2) is the fifth power.

2.Division. Divide by the power of the same base, the base does not change, and the exponent is subtracted: a m a n=a (m-n) (m, n are integers and a≠0).

For example, a 5 a 2 = a (5-2) = a 3, it means that a m is the m power of a, a n is the n power of a, a (m+n) is the m+n power of a, and a (m-n) is the m-n power of a.

3.Computational properties.

1) General form.

The general form of exponential power of a negative integer is a (-n) (a≠0, n is a positive integer).

4.Significance. The meaning of exponential power of a negative integer is:

The -n power (n is a positive integer) power of any number that is not zero is equal to the reciprocal of the n-power of this number.

i.e. a (-n) = 1 (a n).

0 exponential power. The power of 0 of any non-0 real number is equal to 1.

Exponential power of negative real numbers.

The general form of exponential power of negative real numbers is a (-p) = 1 (a) p or (1 a) p (a≠0, p is a positive real number).

Proof that a (-n) = a (0-n) = a 0 a n, because a 0 = 1, a (-n) = a (0-n) = 1 a n, (a≠0, p is a positive real number).

With the introduction of negative exponential powers, the arithmetic properties of exponential powers of positive integers ( still applicable:

a^m)·(a^n)= a^(m+n) ①

That is, multiply with the power of the base, the base does not change, and the exponents are added.

a^m)^n = a^(mn) ②

That is, the power of power, the base does not change, and the exponents are multiplied.

ab)^n=(a^n)(b^n) ③

i.e. the power of the product, multiplying the factors separately.

a^m)÷(a^n)=a^(m-n) ④

That is, the power of the same base is divided, the base is unchanged, and the exponent is subtracted.

a/b)^n=(a^n)/(b^n) ⑤

That is, the power of fractions, multiplying the numerator and denominator respectively.

The same base powers are the same powers. There are a total of 5 computational properties between the same base powers, which are applicable to both spring or positive exponential powers and negative exponential powers.

Exponential computation——

Multiplication. (1) Multiply with the power of the base, the base does not change, and the exponents are added: a m a n=a (m+n)) (m and n are integers).

For example, a 5·a 2 = a (5+2) = a 7For example, the negative quadratic of a multiplied by the negative cubic of a is equal to the negative fifth power of a. The power of a multiplied by the power of a is equal to the power of a.

If it is not the same base, it should be changed to the same base first, pay attention to the symbol).

2) 1. The power of the same base refers to the power of the same base.

For example, (-2) is the power of the fifth and (-2) is the fifth power.

Same as base. The power is the base number is the same as the sun egg.

Multiply (divide) by the power of the bottom front, the base does not change, and the exponent is added (subtracted):

a^m×a^n=a^(m+n)

a^m÷a^n=a^(m-n)

a m = a * a * a multiplication).

a^0=1(a≠0)

a)^0=1(a≠0)

The power of the same base means that the base number is the same.

With the power of the base number of the mountain multiplication (except for the stupid brother), the base number does not carry the change of caution, and the exponent is added (minus):

a^m×a^n=a^(m+n)

a^m÷a^n=a^(m-n)

a m = a * a * a multiplication).

a^0=1(a≠0)

a)^0=1(a≠0)

1. Same base.

A power is a power with the same base. There are 5 computational properties between the powers of the same bottom front, positive exponential power and negative exponential power.

Both apply. 2. Base, a mathematical term, refers to n in power (n m), or logarithm.

x=logan) (a>0 and a is not equal to 1). For example, in 9 32, the base number is 3; 3 log2 8 in Yindan, the number of celebrations at the bottom is 2.

3. The same base is the same base.

Power of the same base operation: multiply the power of the same base, the base does not change, and the exponents are added. Divide by the power of the same base, the base does not change, and the exponent is subtracted:

The power of the power, the base is unchanged, and the exponents are multiplied.

Definition of the same base Huai Sun Mi: The base of multiple powers is the same.

Multiplication of powers of the same base: a m a n=a (m+n)) (m and n are integers). The premise of multiplication to the power of the same base is "same base", and the base can be a specific number or letter, or a monomial or polynomial.

Formulas for power-of-the-same basesThe index plus or minus the base remains unchanged, multiplying and dividing by the power of the base.

The multiplication base of the exponent is unchanged, and the power of the power should be clear.

The product quotient is squared by the original exponent, and the bottom is multiplied by the submergence and then multiplied by the trapped reed.

A non-zero power of a non-zero number, with a constant value of 1 is not confused.

The exponential power of a negative integer, the exponent turns positive to find the reciprocal.

When you see the exponential power of the fraction, you must think that the final number must not be negative.

The power exponent is the numerator, and the root exponent is the denominator.