EVALUATING EXPRESSIONS WITH EXPONENTS

Example 1 :

Evaluate :

(-1)⁴

Solution :

Order of operations (PEMDAS) dictates that parentheses take precedence.

Here, the exponent 4 is an even number. So, the negative sign inside the parentheses will become positive.

When 1 is multiplied by itself any number of times, the result will be 1.

More clearly,

(-1)⁴ = (-1) ⋅ (-1) (-1) ⋅ (-1)

(-1)⁴ = 1

So, the value of (-1)⁴ is 1.

Example 2 :

Evaluate :

(-1)⁵

Solution :

Order of operations (PEMDAS) dictates that parentheses take precedence.

Here, the exponent 5 is an odd number. So, the negative sign inside the parentheses will remain same.

When 1 is multiplied by itself any number of times, the result will be 1.

More clearly,

(-1)⁵ = (-1) ⋅ (-1) ⋅ (-1) ⋅ (-1) ⋅ (-1)

(-1)⁴ = -1

So, the value of (-1)⁵ is -1.

Example 3 :

Evaluate :

-(-3)³

Solution :

Order of operations (PEMDAS) dictates that parentheses take precedence.

So, we have

-[(-3)³] = -[(-3) ⋅ (-3) ⋅ (-3)]

-[(-3)³] = -[-27]

-[(-3)³] = 27

So, the value of (-3)³ is 27.

Example 4 :

Evaluate :

5⁰

Solution :

Anything to the power zero is equal to 1.

So, we have

5⁰ = 1

So, the value of 5⁰ is 1.

Example 5 :

Evaluate :

-3⁰

Solution :

Anything to the power zero is equal to 1.

So, we have

-3⁰ = -1

So, the value of -3⁰ is -1.

Example 6 :

Evaluate :

(-7)⁰

Solution :

Order of operations (PEMDAS) dictates that parentheses take precedence.

Anything to the power zero is equal to 1.

So, we have

(-7)⁰ = 1

So, the value of (-7)⁰ is -1.

Example 7 :

Evaluate :

5^-3

Solution :

Using laws of exponents, we have

5^-3 = 1/5³

5^-3 = 1/125

So, the value of 5^-3 is 1/125.

Example 8 :

Evaluate :

2³ ⋅ 3² ⋅ (-1)⁵

Solution :

In the above expression, first evaluate each term separately.

2³ = 2 ⋅ 2 ⋅ 2 = 8

3² = 3 ⋅ 3 = 9

(-1)⁵ = (-1) ⋅ (-1) ⋅ (-1) ⋅ (-1) ⋅ (-1) = -1

Now, we have

2³ ⋅ 3² ⋅ (-1)⁵ = 8 ⋅ 9 ⋅ (-1)

2³ ⋅ 3² ⋅ (-1)⁵ = - 72

So, the value 2³ ⋅ 3² ⋅ (-1)⁵ is -72.

Example 9 :

Evaluate :

(-1)⁴ ⋅ 3³ ⋅ 2²

Solution :

In the above expression, first evaluate each term separately.

(-1)⁴ = (-1) ⋅ (-1) ⋅ (-1) ⋅ (-1) = 1

3³ = 3 ⋅ 3 ⋅ 3 = 27

2² = 2 ⋅ 2 = 4

Now, we have

(-1)⁴ ⋅ 3³ ⋅ 2² = 1 ⋅ 27 ⋅ 4

(-1)⁴ ⋅ 3³ ⋅ 2² = 108

So, the value (-1)⁴ ⋅ 3³ ⋅ 2² is 108.

Example 10 :

If x²y³  =  10 and x³y²  =  8, then find the value of x⁵y⁵.

Solution :

x²y³ = 10 ----(1)

x³y² = 8 ----(2)

Multiply (1) and (2) :

(1) ⋅ (2) ----> (x²y³) ⋅ (x³y²) = 10 ⋅ 8

x⁵y⁵ = 80

So, the value x⁵y⁵ is 80.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.