Informative line

# 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 $$\leftarrow x^{y\rightarrow\,power}$$

#### 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.

#### 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 $$10×10×10$$

#### 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 $$4^5$$.

#### 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 $$3^4\,2^3$$

#### 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 $$6×6×7×7×7×7$$

#### 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