**Evaluate exponents :**

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

**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

After having gone through the stuff given above, we hope that the students would have understood "Evaluate exponents".

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