SBP-Program

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Exponents with negative bases and negative powers

How to solve problems related to exponents with negative bases and powers?

See the following examples.

Evaluate exponents

Problem 1: Evaluate the exponent with the negative base and power

(-3)-5

Solution:

(-3)-5 = 1 = – 1
(-3)5243

See Powers of 3.

Problem 2: Evaluate the exponent with negative base and negative power

(-3)-6

Solution:

(-3)-6 = 1 = 1
(-3)6729

See Powers of 3.

Problem 3: Evaluate exponents with different negative bases and the same negative exponent

(-4)-3 * 3-3

Solution:

(-4)-3 * 3-3 =
(-4 * 3)-3 =
(-12)-3 = 
1 = – 1
(-12)31728

Problem 4: Evaluate exponents with the same negative base and negative and positive exponents

(-6)-7 * (-6)2

Solution:

(-6)-7 * (-6)2 =
(-6)-7 + 2 =
(-6)-5 = 
1 = –1
(-6)57776

See Powers of 6.

Problem 5: Evaluate exponents with different negative bases and the same negative exponent

(-18)-11 ÷ (6)-11

Solution:

(-18)-11 ÷ (6)-11 =
(-18 ÷ 6)-11 =
(-3)-11 = 
1 =  –1
(-3)11177147

See Powers of 3.

Problem 6: Evaluate exponents with negative bases and negative exponents

(-9)-21 ÷ (-9)-18

Solution:

(-9)-21 ÷ (-9)-18 =
(-9)-21 - (-18) =
(-9)-3 = 
1 =  –1
(-9)3729

See Powers of 9.