SIMPLIFYING ALGEBRAIC TERMS WITH EXPONENTS WORKSHEET

Problem 1 :

Find x so that

(-5)x+1 ⋅ (-5)5  =  (-5)7

Problem 2 :

(5/3)-2 ⋅ (5/3)-14  =  (5/3)8x

Problem 3 :

Find x so that

(-2)⋅ (-2)-6  =  (-2)2x-1

Problem 4 :

Simplify

30+31-3-1

Problem 5 :

Simplify

(-125)1/3

Problem 6 :

Simplify

(32)2/5

Problem 7 :

Simplify

(64)5/6

Problem 8 :

Simplify

(81)-3/4

Problem 9 :

Simplify

3pq-1

Problem 10 :

Simplify

(3x ⋅ 9x)/(27)x+2 

Problem 11 :

Simplify

2x ⋅ 8

Problem 12 :

Simplify

5n+2/5n-2

Problem 13 :

Simplify

51+x/5x-1

Problem 14 :

Simplify

8x/16y

Problem 15 :

Simplify

(5t-2)-1

Problem 16 :

Simplify

(xy)3/y-2

Problem 17 :

Simplify

3x-2  =  1/9

Answers

1. Answer :

(-5)x+1 ⋅ (-5)5  =  (-5)7

(-5) x+1+5  =  (-5)7

(-5) x+6  =  (-5)7

x+6  =  7

x  =  7 - 6

x  =  1

So, the value of x is 1.

2. Answer :

(5/3)-2 ⋅ (5/3)-14  =  (5/3)8x

(5/3)-2-14  =  (5/3)8x

(5/3)-16  =  (5/3)8x

-16  =  8x

x  =  -16/8

x  =  -2

So, the value of x is -2.

3. Answer :

(-2)⋅ (-2)-6  =  (-2)2x-1

(-2)3-6  =  (-2)2x-1

(-2)-3  =  (-2)2x-1

2x-1  =  -3

2x  =  -3+1

2x  =  -2

x  =  -1

So, the value of x is -1.

4. Answer :

= 30+31-3-1

=  1 + 3 - (1/3)

=  4 - (1/3)

=  (12-1)/3

=  11/3

The answer is 11/3.

5. Answer :

=  (-125)1/3

-125  =  -5⋅(-5)⋅(-5)  ==>  (-5)3

=  [(-5)3]1/3

=  -5

The answer is -5.

6. Answer :

=  (32)2/5

32  =  2⋅2⋅2⋅2⋅2 ==>  25

=  (25)2/5

=  22

=  4

The answer is 4.

7. Answer :

= (64)5/6

64  =  2⋅2⋅2⋅2⋅2⋅2 ==>  26

=  (26)5/6

=  25

=  32

The answer is 32.

8. Answer :

= (81)-3/4

81  =  3⋅3⋅3⋅3 ==>  34

=  (34)-3/4

=  3-3

=  1/33

=  1/27

The answer is 1/27.

9. Answer :

3pq-1  =  3p/q

The answer is 3p/q.

10. Answer :

(3x ⋅ 9x)/(27)x+2

=  (3x ⋅ 32x)/(33)x+2 

=  (3x+2x)/33(x+2) 

=  3x+2x/33x+6 

=  3(3x-3x-6)

=  3-6

=  1/36

The answer is 1/36.

11. Answer :

2x ⋅ 8

=  2x ⋅ 23

=  2(x+3)

The answer is 2(x+3).

12. Answer :

=  5n+2/5n-2

=  5(n+2)-(n-2)

=  5n+2-n+2

=  54

The answer is 54 or 625.

13. Answer :

=  51+x/5x-1

=  5(1+x)-(1+x)

=  51+x-1-x

=  52

So, the answer is 25.

14. Answer :

=  8x/16y

8  =  23 and 16  =  24

=  23x/24y

=  23x-4y

15. Answer :

=  (5t-2)-1

=  1/5t-2

=  t2/5

16. Answer :

=  (xy)3/y-2

=  x3y3/y-2

=  x3y3⋅ y2

=  x3y5

17. Answer :

3x-2  =  1/32

3x-2  =  13-2

3x-2  =  3-2

x-2  =  -2

x  =  -2+2

x  =  0

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