- Evaluation of power means solving it.
- We can find the value of a power by completing the multiplication and finding the new product.

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

By evaluating, we get:

\(7^3=7×7×7\)

\(=49×7\)

\(=343\)

(ii) \(10^3\)

By evaluating, we get:

\(10^3=10×10×10\)

\(10^3=1000\)

- We can apply different operations on powers.
- We can add the terms having powers.
- For this, first, evaluate each exponent and then perform the operation.

**For example:** \(6^2+4^3\)

First, we will evaluate the exponents

\(=36+64\)

Now, we will add

\(=100\)

Thus, \(6^2+4^3=100\)

- We can apply different operations on powers.
- We can multiply the different terms having different powers.
- For this, first, evaluate the exponents and then multiply them.

**For example:**

\(2^3.3^2\)

First, we will evaluate the exponents.

\(=2×2×2×3×3\)

\(=8×9\)

Now, we will multiply

\(=72\)

Thus, \(2^3.3^2=72\)

- We can apply different operations on powers.
- We can divide different terms having different powers.
- For this, first, evaluate the exponents and then divide them.

**For example: **\(\dfrac{4^2}{2^4}\)

First, simplify the exponents.

Multiples of 4 = 1, 2 and 4

So we can write,

\(\dfrac{4^2}{2^4}=\dfrac{(2×2)^2}{{2}^4}\)

Using the property \((x.y)^a=x^a.y^a\)

\(=\dfrac{2^2×2^2}{2^4}\)

\(=\dfrac{{2}^{(2+2)}}{{2}^4}\) \(\Bigg[\because\, x^a.x^b=x^{a+b}\Bigg]\)

\(=\dfrac{2^4}{2^4}\)

Now, divide

\(=1\)

Thus, \(\dfrac{4^2}{2^4}=1\)

- We can apply different operations on powers.
- We can subtract the terms having powers.
- For this, first, evaluate each exponent and then perform the operation.

**For example: **\(8^3-36\)

First, we will evaluate the exponent

\(=512-36\)

Now, we will subtract

\(=476\)

Thus, \(8^3-36=476\)

- We can show the comparison between two numbers having powers by using greater than, less than or equal to signs.
- For comparison, we use the following three symbols:

> Greater than

< Less than

= Equal to

- There can be three cases while comparing the numbers having positive powers.

**Case 1: **When the base is same but the power is different.

**For example: **\((4)^2\text{_____}(4)^3\)

Since the base is same, so we will compare the powers.

We know that \(2<3\)

Thus,

\((4)^2<(4)^3\)

Hence, when the base is same but the power is different, then the number with larger power is greater.

**Case 2:** When the power is same but the base is different.

**For example:** \((5)^3\text{_____}(10)^3\)

Since the power is same, so we will compare the bases.

We know that \(5<10\)

Thus, \((5)^3<(10)^3\)

Hence, when the power is same but the base is different, then the number with larger base is greater.

**Case 3:** When both base and power are different.

**For example:** \((5)^3\text{_____}(6)^2\)

First, we will evaluate the terms.

\(5^3=5×5×5=125\)

\(6^2=6×6=36\)

Now, we will rewrite the numbers and compare them.

\(125>36\)

Hence, when both power and base are different, we first evaluate each exponent and then compare them.

**Note: **The opening of the symbol is always towards the larger number.

A \(35\)

B \(5\)

C \(3\)

D \(1\)