**How to evaluate powers and exponents :**

Here we are going to see some example problems based on the concept evaluate exponents.

Exponent says that how many times do we have to multiply the base by itself.

For example, let us consider

2³ = 2 x 2 x 2 (we multiply the base "2" three times)

Before going to see example based on the above concept, we have to know about two terms

(i) Base

(ii) Exponent (or) power (or) index

**How to read ?**

We have to read the above question as 5 raised to the power 3, (or) 5 cube.

**Example 1 :**

Evaluate 4³ x 5³

**Solution :**

To evaluate the above expression involving exponents, we have to multiply 4 three times and 5 three times.

= 4 x 4 x 4 x 5 x 5 x 5

= 64 x 125

= 8000

Hence the answer is 8000.

**Example 2 :**

Evaluate 10⁹ ÷ 10⁶

**Solution :**

10⁹ ÷ 10⁶ = 10⁹/10⁶

= 10⁹⁻⁶

= 10³

= 10 x 10 x 10

= 1000

Hence the answer is 1000.

**Example 3 :**

Evaluate (3/2)⁵

**Solution :**

= (3/2)⁵

Distributing the power for both numerator and denominator separately.

= 3⁵/2⁵

= (3 x 3 x 3 x 3 x 3)/(2 x 2 x 2 x 2 x 2)

= 243/32

Hence the answer is 243/32.

**Example 4 :**

Evaluate (3⁴/3⁻³)

**Solution :**

= (3⁴/3⁻³)

Since we have same base for both numerator and denominator, first we have to combine the powers and then we can evaluate the exponent.

= 3^(4 + 3)

= 3^7

= 3 x 3 x 3 x 3 x 3 x 3 x 3

= 21873

Hence the answer is 2187.

**Example 5 :**

Evaluate (4p)³ x (2p)² x p⁴

**Solution :**

= (4p)³ x (2p)² x p⁴

Distributing the powers, we get

= 4³p³ x 2²p²x p⁴

= (4 x 4 x 4) p³ x (2 x 2) p²x p⁴

= 64 p³ x 4 p²x p⁴

= (64 x 4) p^(3 + 2 + 4)

= 256 p^9

Hence the answer is 256 p^9.

**Example 6 :**

Evaluate [(-2/3)^-2]^-2

= [(-2/3)^-2]^-2

When we have power raised to another power, we have to multiply both the powers.

= (-2/3)^-4

To convert the negative power as positive, we have to take a reciprocal of the fraction -2/3

= (-3/2)^4

By distributing the powers, we get

= (-3)^4/2^4

(-3)^4 = -3 x (-3) x (-3) x (-3) = 81

2^4 = 2 x 2 x 2 x 2 = 16

= 81/16

Hence the answer is 81/16

- How to evaluate exponents with integer bases
- How to evaluate integers raised to rational exponents
- Exponents with negative bases
- Exponents with fractional and decimal base

After having gone through the stuff given above, we hope that the students would have understood "How to evaluate powers and exponents".

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