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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
mathsExponentsFundamentals of Exponents

### Representation of Exponents

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What is "multiplication"?

• just another arithmetic operation, not related to addition

Multiplication is learned as repeated addition in whole numbers.
3xx5 is 3 repeated 5 times (or 3 times 5).

Later, multiplication is extended to negative numbers and fractions.
eg: 3xx (-5) is 3 repeated -5 times.
3xx 1/6 is 3 repeated 1/6 times.

We learned meaning of multiplication by whole numbers, negative numbers, and fractions.

Similarly, "exponents" are introduced as repeated multiplication.
3^5 = 3 xx 3 xx 3 xx 3 xx 3.

In this, we learn
•  What is exponent to a whole number, eg : 3^5?
•  What is exponent to a negative number, eg: 3^(-5)?
•  What is exponent to a fraction, eg: 9^(1/2)?

Knowing that exponent is repeated multiplication, which of the following is the exponent 5^2?

• 5xx5
• 5xx5
• 2xx2xx2xx2xx2
• 5xx2=10

The answer is "5xx5"

Which of the following is a meaning for the word "exponent"?

• a number raised to the power of another number
• a number raised to the power of another number
• an attendant in an exhibition

The answer is "a number raised to the power of another number".

Exponent also means "higher level or higher order".

What is the term used to refer "a number raise to the power of another number"?

• Pronunciation : Say the answer once

How do you read the expression 2^3?

• Pronunciation : Say the answer once

The answer is, 2 to the power of 3 or 2 power 3.

Exponents : Exponents are repeated multiplication.

5xx5xx5 = 5^3 = 125
5 is the base
3 is the exponent or the power
125 is the result of exponentiation

Which of the following is a meaning for the word "base"?

• the foundation or lower part of something
• the foundation or lower part of something
• second to an ace

The answer is "the foundation or lower part of something".

What is the term used to refer 2 in 2^5?

• Pronunciation : Say the answer once

What is the term used to refer 5 in 2^5?

• Pronunciation : Say the answer once

The answer is "exponent or power".

What is the value of 2^5?

• 32
• 32
• 25
• 10

The answer is "32".

2^5
=2 xx 2 xx 2 xx 2 xx 2
=32

Which of the following is 3xx3xx3xx3?

• 4^3
• 3^4
• 3^4

The answer is "3^4".

What is the value of 2^(-3)?

• 1/8
• 1/8
• exponent of negative number is not possible

The answer is "1/8".

Integer 3 is text(aligned:)3 in directed whole number form. To compute 2^3, in the aligned direction, starting from 1, multiply in ratio of base 2. It progresses in the following order
2, 2xx2, 2xx2xx2

Integer -3 is text(opposed:)3 in directed whole number form. To compute 2^(-3), in the opposed direction, starting form 1 divide in ratio of base 2. It progresses in the following order 1/2, 1/(2xx2), 1/(2xx2xx2).

Which of the following is 1/(3xx3xx3xx3)?

• (-4)^3
• 3^(-4)
• 3^(-4)

The answer is "3^(-4)"

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