Informative line

Representation Of Base And Exponents

Power and Base

Power of a number

  • Power of a number denotes the value upto which the number is multiplied by itself.
  • It is written at the top right of a number.
  • Power is also known as exponent.

Example: \(6^2\)

Here, \(2\) is written at top right.

Thus, \(2\) is the power.

Base

  • Base is the number on which power is raised.

Example: \(6^2\)

Here, \(6\) is base.

base \(\leftarrow x^{y\rightarrow\,power}\)

Illustration Questions

What is the power in the given term, \(5^3\)?

A \(5\)

B \(3\)

C Both

D None of these

×

Power is written at the top right of a number.

In \(5^3\)\(3\) is written at top right.

Thus, \(3\) is the power.

Hence, option (B) is correct.

What is the power in the given term, \(5^3\)?

A

\(5\)

.

B

\(3\)

C

Both

D

None of these

Option B is Correct

Representation of Power

  • Bases and exponents can be read in form of statements.
  • When power is written at the top right of a number then we read it as number to the power.

For example:

(a) \(3^5\) is read as three to the fifth power.

(b) \(5^8\) is read as five to the eighth power.

  • When the power of base is \(2\) we read it as "base squared".

For example:

(a) \(6^2\) is read as six squared.

(b) \(7^2\) is read as seven squared.

  • When the power of base is \(3\) we read it as "base cubed".

For example:

(a) \(2^3\) is read as two cubed.

(b) \(4^3\) is read as four cubed.

Illustration Questions

How will you write "Six to the eighth power"?

A \(6^8\)

B \(8^6\)

C \(8×6\)

D \(8+6\)

×

Here, base is \(6\) and power is \(8\).

Thus, we write it as \(6^8\).

Hence, option (A) is correct.

How will you write "Six to the eighth power"?

A

\(6^8\)

.

B

\(8^6\)

C

\(8×6\)

D

\(8+6\)

Option A is Correct

Expanded Form

  • A number with a power can be written in expanded form.
  • Expanded form is also known as product of repeating factors.
  • We will multiply the number by itself up to the value of power.

For example: \(10^3\)

Here, power is \(3\), so we multiply \(10\) by itself \(3\) times.

Also, the repeating factor is \(10\), so the product of repeating factor \(10\) can be written as \(10×10×10\) 

Illustration Questions

What is the expanded form of the given term: \(3^6\)?

A \(3×6\)

B \(6×6×6\)

C \(3×3×3×3×3×3\)

D \(3+6\)

×

In expanded form, we multiply the number by itself up to the value of power.

Here, power is \(6\), so we multiply \(3\) by itself \(6\) times.

Thus, the expanded form of \(3^6\) is \(3×3×3×3×3×3\) 

Hence, option (C) is correct.

What is the expanded form of the given term: \(3^6\)?

A

\(3×6\)

.

B

\(6×6×6\)

C

\(3×3×3×3×3×3\)

D

\(3+6\)

Option C is Correct

Exponential Form

  • The expanded form or the product of repeating factors can be written in a simple way known as exponential form.
  • In this, we count the number of times a number is multiplied by itself and write it as the power of that number.
  • For Example: \(4×4×4×4×4\)

Here, \(4\) is multiplied \(5\) times by itself.

Thus, the power of \(4\) is \(5\).

Hence, we write it as \(4^5\).

Illustration Questions

What is the exponential form of the following term? \(2×2×2×2×2×2×2\)

A \(2×7\)

B \(2^7\)

C \(7^2\)

D \(2+7\)

×

To write an exponential term, first count the number of times a number is multiplied by itself and then write it as the power of that number.

Here, \(2\) is multiplied \(7\) times by itself.

Thus, the power of \(2\) is \(7\).

Hence, we write it as \(2^7\).

Hence option (B) is correct.

What is the exponential form of the following term? \(2×2×2×2×2×2×2\)

A

\(2×7\)

.

B

\(2^7\)

C

\(7^2\)

D

\(2+7\)

Option B is Correct

Writing the Product of Repeating Factors in Exponential Form

  • The product of repeating factors can be written in exponential form.
  • In this, we count the number of times a number is multiplied by itself and write it as the power of that number.

For example: \(3×3×3×3×2×2×2\)

Here, \(3\) is multiplied \(4\) times by itself and \(2\) is multiplied \(3\) times by itself.

Thus, the power of \(3\) is \(4\) and the power of \(2\) is \(3\).

Here, we write it as \(3^4\,2^3\)

Illustration Questions

What is the exponential form of the following term? \(4×4×5×5×5\)

A \(4×5\)

B \(2×3\)

C \(4^2\,5^3\)

D \(2^4\,3^5\)

×

To write an exponential form, count the number of times a number is multiplied by itself and write it as the power of that number.

Here, \(4\) is multiplied 2 times by itself and \(5\) is multiplied 3 times by itself.

Thus, the power of \(4\) is \(2\) and power of \(5\) is \(3\).

Thus, the exponential form is \(4^2\,5^3\).

 

Hence, option (C) is correct.

What is the exponential form of the following term? \(4×4×5×5×5\)

A

\(4×5\)

.

B

\(2×3\)

C

\(4^2\,5^3\)

D

\(2^4\,3^5\)

Option C is Correct

Writing Expanded Form from Exponential Form

  • The power of numbers can be written in expanded form.
  • We multiply the number by itself up to the value of the power.

For example: \(6^2\,7^4\)

Here, the power of \(6\) is  \(2\) and the power of  \(7\)  is  \(4\).

Thus, 6 should be multiplied two times by itself and \(7\) should be multiplied four times by itself.

Hence, the expanded form is \(6×6×7×7×7×7\) 

Illustration Questions

What is the expanded form of the given term \(2^3\,4^2\)?

A \(2×3×4×2\)

B \(3×2\)

C \(2×4\)

D \(2×2×2×4×4\)

×

To write the expanded form, we multiply the number by itself up to the value of power.

Here, the power of \(2\) is \(3\) and the power of \(4\) is \(2\).

Thus, \(2\) should be multiplied three times by itself and \(4\) should be multiplied two times by itself.

Hence, the expanded form is \(2×2×2×4×4\)

Hence, option (D) is correct.

What is the expanded form of the given term \(2^3\,4^2\)?

A

\(2×3×4×2\)

.

B

\(3×2\)

C

\(2×4\)

D

\(2×2×2×4×4\)

Option D is Correct

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