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Definition of power to a power

What is the definition of power to a power in math? What is the meaning of power of a power?

Definition

The definition of power to a power is simple.

Definition of power to a power:

Power of a power is a power with the same base and its exponent is equal to the product of the exponents.

Power of a power formula

Power of a power formula

(am)n = am * n

Examples of power of a power

Example 1.

Power of a power

(42)3 =
42 * 3 =
46 = 4096

See Powers of 4.

Example 2.

A power with a positive base and a negative exponent of a positive power

(4-2)3 =
4-2 * 3 =
4-6 =
1 = 1
464096

See Powers of 4.

Example 3.

A power with a positive base and a positive exponent of a negative power

(42)-3 =
42 * (-3) =
4-6 =
1 = 1
464096

See Powers of 4.

Example 4.

A power with a positive base and a negative exponent of a negative power

(4-2)-3 =
4-2 * (-3) =
46 = 4096

See Powers of 4.