- The power of a variable denotes the value up to which the variable is multiplied by itself.
- It is written at the top right of a number.

**Example:** \(x^2\)

Here, \(2\) is written at the top right of \(x\).

Thus, the power of \(x\) is 2.

- The power is also known as an exponent or an index.

- The base is the variable on which power is raised.

**Example:** \(z^4\)

Here, the base is \(z\).

**Note**: Instead of writing \(y^1\), we write only \(y\).

- An exponent can be written in product form.
- In product form, we multiply the literal with itself repeatedly up to the value of power.

**For example: \(a^7\)**

Here, the power is \(7\), so ' \(a\)' is to be multiplied \(7\) times by itself.

Product form: \(a×a×a×a×a×a×a\)

A \(c× 4\)

B \(c × c × c × c\)

C \(c+c+c+c\)

D \(4^c\)

- The expression in which more than one variable is used can also be written in an exponential form.
- In this, we count the number of times a variable is repeatedly multiplied by itself and write it as a power of that literal.

**For example:** \(b×b×c×c×c\)

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

Thus, the exponential form is

\(b^2c^3\)

A \(abc\)

B \(a×2×b×c×3\)

C \(a^2bc^3\)

D None of these

- The expression in which more than one variable is used can also be written in product form.
- For the product form, we multiply a variable repeatedly by itself up to the value of the power of that variable.

**For example:** \(x^3 y^2z\)

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

Thus, \(x\) should be multiplied by itself up to \(3\) times and \(y\) should be multiplied by itself up to \(2\) times.

Hence, the product form is:

\(x×x×x×y×y×z\)

A \(\ell mn\)

B \(\ell ×m×2×n×4\)

C \(\ell ×m\)

D \(\ell ×m×m×n×n×n×n\)

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

**For example:**

\(m× m× m× m× m\)

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

Thus, we write it as \(m^5\).

- \(n× n\) is written as \(n^2\) and is called \(n\) squared.
- \(n× n× n\) is written as \(n^3\) and is called \(n\) cubed.
- \(n× n× n× n\) is written as \(n^4\) and is called \(n\) raised to the power \(4\).
- \(n× n× n× n× n\) is written as \(n^5\) and is called \(n\) raised to the power \(5\) and so on.

A \(s^9\)

B \(s×9\)

C \(s\)

D \(9\)

- Numbers are used along with variables.
- The expressions involving the product of numbers and variables can be written in exponential form.
- In this, we count the number of times a variable is multiplied by itself and write it as the power of that variable.

**For example:** \(4×a×a×b×c×c×c\)

Here, \(a\) is multiplied \(2\) times with itself, \(b\) is multiplied once and \(c\) is multiplied \(3\) times with itself.

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

A \(5w\ell b\)

B \(w\ell b\)

C \(5 w^4 \ell ^2 b^5\)

D \(w×4×\ell ×2×b×5\)

- Numbers are used along with variables.
- The expressions involving numbers and variables having powers can be written in product form.
- For the product form, we multiply a variable by itself up to the value of the power of that variable.

**For example:** \(7 abc^3\)

Here, the power of \(c\) is \(3\).

Thus, in product form, \(c\) should be multiplied \(3\) times by itself.

Hence, the product form is \(7× a × b × c× c× c\)

A \(2× x× 2× y× 3× z\)

B \(x^2 yz^3\)

C \(2× xyz\)

D \(2× x× x× y× z× z×z\)