How to multiply degrees

In mathematics, there is such a thing as a degree. A degree is a product of several equal factors. The degree has a basis equal to one of such factors. There is also an indicator of the degree to which one of these factors is being constructed. For example, 2³ = 2 * 2 * 2 = 16, where 2 is the basis of the degree, and 3 is its indicator. Various simplifications are possible in the multiplication of degrees among themselves. For this, this instruction is proposed.

Instruction manual

one

We determine the degrees of what kind are multiplied. If the members of such a product have the same degree bases, and the exponents are not the same, for example, 2² * 2³, then the result will be a degree basis with the same equal base of the members of the degrees raised to a degree index equal to the sum of the indicators of all multiplied degrees.

I.e

2² * 2³ = 2²⁺³ = 2⁵ = 32

2

If the members of the product of degrees have different degree bases, and the exponents are the same, for example, 2³ * 5³, then the result will be the product of the bases of these degrees raised to an exponent equal to this same exponent.

I.e

2³ * 5³ = (2 * 5) ³ = 10³ = 1000

3

If the multiplied degrees are equal to each other, for example, 5³ * 5³, then the result will be a degree with a base equal to these identical degree bases, raised to an exponent equal to the exponent multiplied by the number of these identical degrees.

I.e

5³ * 5³ = (5³) ² = 5³ * ² = 5⁶ = 15625

Or another example with the same result:

5² * 5² * 5² = (5²) ³ = 5² * ³ = 5⁶ = 15625

• What is a degree with a natural indicator
• product of degrees