EVALUATING EXPRESSIONS WITH EXPONENTS WORKSHEET

Problem 1 :

Evaluate : 

(-1)4

Problem 2 :  

Evaluate : 

(-1)5

Problem 3 : 

Evaluate : 

-(-3)3

Problem 4 : 

Evaluate : 

50

Problem 5 : 

Evaluate : 

-30

Problem 6 : 

Evaluate : 

(-7)0

Problem 7 : 

Evaluate : 

5-3

Problem 8 : 

Evaluate : 

23 ⋅ 3⋅ (-1)5

Problem 9 : 

Evaluate : 

(-1)4 ⋅ 3⋅ 22

Problem 10 : 

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

Detailed Answer Key

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)=  (-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 : 

50

Solution : 

Anything to the power zero is equal to 1. 

So, we have

50  =  1

So, the value of 50 is 1.

Problem 5 : 

Evaluate : 

-30

Solution : 

Anything to the power zero is equal to 1. 

So, we have

-30  =  -1

So, the value of -3is -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)is -1.

Problem 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.

Problem 8 : 

Evaluate : 

23 ⋅ 3⋅ (-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 ⋅ 3⋅ (-1)5  =  8 ⋅ 9 ⋅ (-1)

23 ⋅ 3⋅ (-1)5  =  - 72

So, the value 23 ⋅ 3⋅ (-1)5 is -72.

Problem 9 : 

Evaluate : 

(-1)4 ⋅ 3⋅ 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 ⋅ 3⋅ 22  =  1 ⋅ 27 ⋅ 4

(-1)4 ⋅ 3⋅ 22  =  108

So, the value (-1)4 ⋅ 3⋅ 22 is 108.

Problem 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.

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