Exponents and Their Applications

The video tutorial explains how to simplify problems involving decimal powers and exponents, which are common in quantitative aptitude exams. It covers converting decimals to fractions, using prime factorization, and applying laws of exponents to solve problems efficiently. The tutorial also addresses handling reciprocal bases and provides tips for exam preparation.

Why are decimal powers considered challenging in exams?

• They are rarely used in real life.

• They test comfort with decimals.

• They involve complex calculations.

• They are not covered in textbooks.

What is the first step in simplifying 16 raised to the power of 1.5?

• Convert 16 to a decimal.

• Factorize 16 into prime factors.

• Multiply 16 by 1.5.

• Divide 16 by 1.5.

How can 1.5 be expressed as a fraction?

• 2/3

• 1/2

• 5/2

• 3/2

What is the simplified form of 81 raised to the power of 0.25?

• 27

• 81

• 3

• 9

What is the result of 2 raised to the power of 6 multiplied by 3?

• 192

• 128

• 64

• 256

In the second problem, what happens when two terms with the same base are multiplied?

• The exponents are divided.

• The exponents are subtracted.

• The exponents remain unchanged.

• The exponents are added.

How is 3.5 expressed as a fraction?

• 3/2

• 7/3

• 7/2

• 5/2

What is the simplified result of 2 raised to the power of 8 divided by 2 raised to the power of 7?

• 1

• 2

• 3

• 0

In the third problem, what is the first step in dealing with a larger base like 252?

• Multiply it by 2.5.

• Factorize it into prime factors.

• Convert it to a decimal.

• Divide it by 2.5.

What is the result of 7 raised to the power of 5/2 minus 1/2?

• 1

• 7

• 49

• 343