**Evaluating Expressions with Exponents Worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on evaluating expressions with exponents.

To evaluate expression with exponents, we need to be aware of laws of exponents.

To know more about laws of exponents,

**Problem 1 :**

Evaluate :

(-1)^{4}

**Problem 2 : **

Evaluate :

(-1)^{5}

**Problem 3 : **

Evaluate :

-(-3)^{3}

**Problem 4 : **

Evaluate :

5^{0}

**Problem 5 : **

Evaluate :

-3^{0}

**Problem 6 : **

Evaluate :

(-7)^{0}

**Problem 7 : **

Evaluate :

5^{-3}

**Problem 8 : **

Evaluate :

2^{3} ⋅ 3^{2 }⋅ (-1)^{5}

**Problem 9 : **

Evaluate :

(-1)^{4} ⋅ 3^{3 }⋅ 2^{2}

**Problem 10 : **

If x^{2}y^{3} = 10 and x^{3}y^{2} = 8, then find the value of x^{5}y^{5}.

**Problem 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.

**Problem 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.

**Problem 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.

**Problem 4 : **

Evaluate :

5^{0}

**Solution : **

Anything to the power zero is equal to 1.

So, we have

5^{0} = 1

So, the value of 5^{0 }is 1.

**Problem 5 : **

Evaluate :

-3^{0}

**Solution : **

Anything to the power zero is equal to 1.

So, we have

-3^{0} = -1

So, the value of -3^{0 }is -1.

**Problem 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.

**Problem 7 : **

Evaluate :

5^{-3}

**Solution : **

Using laws of exponents, we have

5^{-3} = 1 / 5^{3}

5^{-3} = 1 / 125

So, the value of 5^{-3}^{ }is 1/125.

**Problem 8 : **

Evaluate :

2^{3} ⋅ 3^{2 }⋅ (-1)^{5}

**Solution : **

In the above expression, first evaluate each term separately.

2^{3} = 2 ⋅ 2 ⋅ 2 = 8

3^{2} = 3 ⋅ 3 = 9

(-1)^{5 }= (-1) ⋅ (-1) ⋅ (-1) ⋅ (-1) ⋅ (-1) = -1

Now, we have

2^{3} ⋅ 3^{2 }⋅ (-1)^{5} = 8 ⋅ 9^{ }⋅ (-1)

2^{3} ⋅ 3^{2 }⋅ (-1)^{5} = - 72

So, the value 2^{3} ⋅ 3^{2 }⋅ (-1)^{5 }is -72.

**Problem 9 : **

Evaluate :

(-1)^{4} ⋅ 3^{3 }⋅ 2^{2}

**Solution : **

In the above expression, first evaluate each term separately.

(-1)^{4 }= (-1) ⋅ (-1) ⋅ (-1) ⋅ (-1) = 1

3^{3} = 3 ⋅ 3 ⋅ 3 = 27

2^{2} = 2 ⋅ 2 = 4

Now, we have

(-1)^{4} ⋅ 3^{3 }⋅ 2^{2 }= 1 ⋅ 27^{ }⋅ 4

(-1)^{4} ⋅ 3^{3 }⋅ 2^{2 }= 108

So, the value (-1)^{4} ⋅ 3^{3 }⋅ 2^{2}^{ }is 108.

**Problem 10 : **

If x^{2}y^{3} = 10 and x^{3}y^{2} = 8, then find the value of x^{5}y^{5}.

**Solution : **

x^{2}y^{3} = 10 -----(1)

x^{3}y^{2} = 8 -----(2)

Multiply (1) and (2) :

(1) ⋅ (2) -----> (x^{2}y^{3}) ⋅ (x^{3}y^{2}) = 10 ⋅ 8

x^{5}y^{5} = 80

So, the value x^{5}y^{5 }is 80.

After having gone through the stuff given above, we hope that the students would have understood, "Evaluating Expressions with Exponents Worksheet".

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