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Dividing exponents with the same base and exponents

How do you divide exponents with the same base and exponents?

See the following examples.

Examples of dividing exponents with the same base and exponents

Example 1.

Dividing exponents with the same base and exponents

510 ÷ 510 =
510 - 10 =
150 = 1

Or shorter

510 ÷ 510 = 1

See Powers of 5.

Example 2.

Dividing powers with the same base and exponent

612 ÷ 612 =
612 - 12 =
60 = 1

Or shorter

612 ÷ 612 = 1

Example 3.

Dividing powers with the same base and different negative exponents

7-15 ÷ 7-10 =
7-15 - (-10) =
7-15 + 10 =
7-5 =
1/75 = 1/16807

See Powers of 7.

Example 4.

Dividing exponents with the same base and negative exponents

(-9)-26 ÷ (-9)-26 =
(-9)-26 - (-26) =
(-9)-26 + 26 =
(-9)0 = 1

Or shorter

(-9)-26 ÷ (-9)-26 = 1

Example 5.

Division of exponents with the same base and unequal exponents

(-8)25 ÷ (-8)22 =
(-8)25 - 22 =
(-8)3 = -512

See Powers of 8.