Exponents and Powers Concepts

Amal Kumar explains how to solve exponential equations involving decimals and fractions. The video covers two examples: solving 2^x = 0.25 by converting decimals to fractions and solving 7^(1/2x - 3) = 1 using the property that any number to the power of zero equals one. The video emphasizes the importance of expressing numbers with the same base to simplify and solve the equations.

What is the first step in solving exponential equations with decimals?

• Convert decimals to fractions

• Multiply both sides by 10

• Add 1 to both sides

• Divide both sides by 2

How can 0.25 be expressed as a fraction?

• 1/2

• 1/4

• 1/5

• 1/10

What is the equivalent of 0.25 in terms of powers of 2?

• 2^-2

• 2^-1

• 2^0

• 2^1

What is the solution to the equation 2^x = 0.25?

• x = 0

• x = 1

• x = -2

• x = 2

What is the base of the equation 2^x = 0.25?

• 2

• 4

• 1

• 0.25

What operation is used to solve 2^x = 1/4?

• Addition

• Subtraction

• Reciprocal

• Multiplication

What is the reciprocal of 2^2?

• 1/4

• 1/16

• 1/2

• 1/8

What is the exponent of 2 when 2^-2 equals 1/4?

• 0

• -2

• 1

• 2

How can the number 1 be expressed as a power of 7?

• 7^1

• 7^0

• 7^2

• 7^-1

What should 1/2x - 3 equal to solve the equation 7^(1/2x - 3) = 1?

• 1

• 2

• 3

• 0