What is the algorithm for the same exponents but different bases?

The exponents are the sameBaseDifferent algorithms: a n*b n=(a*b) n.

In fact, this is a power operation, for example: a 5·a 2=a (5+2)=a 7, for example, the negative quadratic of a multiplied by the negative power of a is equal to the negative fifth power of a. A to the power of 0.

Multiplying a to the power of 0 is equal to the power of 0 of a, if it is not the same base, it should be changed to the same base first, pay attention to the symbol.

Power Algorithm Formula:Multiplication to the power of the same base: the power of the power of the exponent without the same base.

Division to the power of the same base: the base is unchanged, and the exponent is subtracted to the power of the power;

exponential power of power: equal to the power of the product quotient of each factor of the respective power;

Fractional. Powers: The numerator and denominator are multiplied separately, and the exponent is unchanged.

When the exponents are the same but the bases are different, the following algorithm can be used:

1.Multiplication: If the exponents are the same but the bases are different, you can multiply the bases and keep the exponents the same. i.e., a x * b x = (a * b) x.

For example, 2 3 * 3 3 = (2 * 3) 3 = 6 3.

2.The rule of division: If the exponents are the same but the bases are different, you can divide the bases and keep the exponents unchanged. i.e., a x * b x = (a * b) x.

For example, 4 2 2 2 = (4 2) 2 = 2 2.

3.Power rule: If the exponents are the same but the bases are different, you can power the bases and keep the exponents unchanged. i.e., (a m) x = a (m * x).

For example, (2 3) 2 = 2 (3 * 2) = 2 6.

These algorithms are applicable when the exponents are the same but the bases are different. They allow us to combine and simplify different bases when doing exponential operations. These rules are often used in mathematics and science to simplify expressions, solve problems, and simplify calculations.

When the exponents are the same but the bases are different, we can use the following algorithm:

1.Multiply bases: When exponential powers of the same have different bases, they can be multiplied by their bases and leave the exponents unchanged. For example, a m * b m = (a * b) m.

2.Base division: When exponential powers of the same have different bases, you can divide their bases and leave the exponent unchanged. For example, a m * b m = (a * b) m.

3.Base multiplication: When exponents of the same power have different bases, their exponents can be applied to their respective bases and the exponents remain unchanged. For example, a m * b m = (a m) * b m).

These rules apply to operations with powers of the same exponent but different bases, and can help us simplify or combine expressions to powers.

When the exponents are the same but the bases are different, the following algorithm can be used to simplify the calculation:

1.Multiplication rule: If two numbers with the same exponent are multiplied, the base numbers can be multiplied and the exponent remains the same. i.e., a m * b m = (a * b) m.

For example, 2 3 * 3 3 = (2 * 3) 3 = 6 3 = 216.

2.The rule of division: If two numbers with the same exponent are divided, the base can be divided and the exponent remains the same. i.e., a m * b m = (a * b) m.

For example, 4 5 2 5 = (4 2) 5 = 2 5 = 32.

3.The power rule of powers: If the exponents of the same number are multiplied, the base remains the same and the exponents are multiplied. i.e., (a m) n = a (m * n).

For example, (2 3) 4 = 2 (3 * 4) = 2 12.

It should be noted that the above algorithm applies to the case where the indices are the same but the bases are different. When applied, the appropriate law can be selected for calculation according to the specific problem and calculation needs, so as to simplify the calculation and obtain the result.

The algorithm for the same exponents with different bases is a n*b n=(a*b) n. The operation rule of the index is the same, the base is different, addition and subtraction have no operation rule, the operation rule of multiplication, that is, their bases are different means that they belong to the product of the product of the product, it is also an inverse operation, and there is the division operation, that is, the base cannot be 0, when dividing, it is the power of the quotient, which is equal to the quotient of the power.

Power Algorithm Formula:Multiplication of the same power of the base, the base is constant, the power of the exponent is added, the division of the same power of the base, the base is constant, the power of the exponent is subtracted to the power, the exponential power is the power of the exponent, the product quotient equal to the power of each factor, the power of the fraction, the numerator and the denominator are multiplied respectively, and the exponent is constant.

Here the same base of the exponent is different from the product of the product, that is to say, their product is equal to the product of the base, that is, the product of the product is equal to the multiplication of the base, that is, the product of the product is equal to the product of the product, and when the same division is the index of the division of the base, the addition and subtraction cannot be calculated.

BaseNo, the whole formula with the same exponent.

Multiplication algorithm: a n b n = (a b) n

This type of operation is called a power operation. For example:

In addition, there is a multiplication operation with different exponents of the same base: n a n b = n (a+b).

Example of Sun Qinru:

The algorithm for the same exponents with different bases is a n*b n=(a*b) n. The operation rule of the index is the same, the base is different, addition and subtraction have no operation rule, the operation rule of multiplication, that is, their bases are different means that they belong to the product of the product of the product, it is also an inverse operation, and there is the division operation, that is, the base cannot be 0, when dividing, it is the power of the quotient, which is equal to the quotient of the power.

Power Algorithm Formula:Multiplication of the same base power, the closing of the banquet base is unchanged, the power of the exponential addition, the division of the same base power, the base is unchanged, the power of the exponential subtraction, the exponential power of the power, the power of the product quotient equal to the power of each factor, the power of the factor, the power of the numerator and the denominator, the exponent is unchanged.

Here the same base of the exponent is different is the product of the product, that is to say, their product is equal to the product of the base of the mu of the product of the power of the product, that is, the product of the product is equal to the base of the multiplication of the exponential change, that is, the product of the product is equal to the product of the product, the same division is the base division of the exponent unchanged, as for the addition and subtraction can not be operated on the silver of the car.

The algorithm for the same exponents with different bases is a n*b n=(a*b) n. The operation rule of the index is the same, the base is different, addition and subtraction have no operation rule, the operation rule of multiplication, that is, their bases are different means that they belong to the product of the product of the product, it is also an inverse operation, and there is the division operation, that is, the base cannot be 0, when dividing, it is the power of the quotient, which is equal to the quotient of the power.

Power Algorithm Formula:Multiplication of the same base power, the closing of the banquet base is unchanged, the power of the exponential addition, the division of the same base power, the base is unchanged, the power of the exponential subtraction, the exponential power of the power, the power of the product quotient equal to the power of each factor, the power of the factor, the power of the numerator and the denominator, the exponent is unchanged.

Here the same base of the exponent is different is the product of the product, that is to say, their product is equal to the product of the base of the mu of the product of the power of the product, that is, the product of the product is equal to the base of the multiplication of the exponential change, that is, the product of the product is equal to the product of the product, the same division is the base division of the exponent unchanged, as for the addition and subtraction can not be operated on the silver of the car.

The integer multiplication algorithm with different bases and the same exponent: a n b n=(a b) n

This type of operation is called a power operation. For example:

Different bases are the same as the index:

Different indices with the same base:

Different indices for different bases:

It can only be left unmoved, or hard calculation.

BaseNo, the whole formula with the same exponent.

Multiplication algorithm: a n b n = (a b) n

This type of operation is called a power operation. For example:

In addition, there are multiplication operations with different exponents of the same base: n a n b = n (a+b) for example:

BaseNo, the whole formula with the same exponent.

Multiplication algorithm: a n b n = (a b) n

This type of operation is called a power operation.

For example: Yard Shirt Branch.

Integer multiplication with different bases and the same exponent: a n b n=(a b) n This operation is called a power operation. For example:

In addition, there are multiplication operations with different exponents of the same base: n a n b = n (a+b) for example: