Understanding Exponential Equations with Negative Bases

The video tutorial explains the exponential equation a^b = c, where a is negative, c is positive, and b is a positive integer. By substituting values for a and b, the video demonstrates that c must be positive, leading to the conclusion that b must be an even number. This is because a negative number raised to an even power results in a positive number.

What is the condition given for the variable 'a' in the exponential equation a^b = c?

• a is a positive integer

• a is equal to zero

• a is less than zero

• a is greater than zero

Which of the following is true about the variable 'b' in the equation a^b = c?

• b is a positive integer

• b is a negative integer

• b is zero

• b is a fraction

Tags

CCSS.6.EE.A.2C

If a = -2 and b = 1, what is the value of c?

• 2

• -2

• 4

• 0

Tags

CCSS.6.EE.A.1

What is the result of -2 raised to the power of 2?

• -4

• 4

• 2

• -2

Why can't b be equal to 3 in the equation a^b = c?

• Because c would be negative

• Because c would be zero

• Because c would be undefined

• Because c would be a fraction

Tags

CCSS.6.EE.A.2C

What is the value of c when b equals 4 and a equals -2?

• 8

• -16

• 16

• -8

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

For which value of b does c equal 64 when a is -2?

• 5

• 8

• 7

• 6

What conclusion can be drawn about the value of b for c to be positive?

• b must be odd

• b must be zero

• b must be even

• b must be a fraction

Why must b be even for a negative base to result in a positive c?

• Because an even power of a negative number is zero

• Because an even power of a negative number is positive

• Because an even power of a negative number is undefined

• Because an even power of a negative number is negative

Tags

CCSS.7.EE.B.4A

Which of the following values of b will result in a positive c when a is -2?

• 1, 3, 5

• 2, 4, 6

• 3, 5, 7

• 1, 2, 3

Tags

CCSS.7.EE.B.4A