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)³ ⋅ (-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

(3^x ⋅ 9^x)/(27)^x+2 

Problem 11 :

Simplify

2^x ⋅ 8

Problem 12 :

Simplify

5ⁿ⁺²/5^n-2

Problem 13 :

Simplify

5^1+x/5^x-1

Problem 14 :

Simplify

8^x/16^y

Problem 15 :

Simplify

(5t^-2)^-1

Problem 16 :

Simplify

(xy)³/y^-2

Problem 17 :

Simplify

3^x-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)³ ⋅ (-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 :

(3^x ⋅ 9^x)/(27)^x+2

=  (3^x ⋅ 3^2x)/(3³)^x+2 

=  (3^x+2x)/3^3(x+2) 

=  3^x+2x/3^3x+6 

=  3^(3x-3x-6)

=  3^-6

=  1/3⁶

The answer is 1/3⁶.

11. Answer :

2^x ⋅ 8

=  2^x ⋅ 2³

=  2^(x+3)

The answer is 2^(x+3).

12. Answer :

=  5ⁿ⁺²/5^n-2

=  5^(n+2)-(n-2)

=  5^n+2-n+2

=  5⁴

The answer is 5⁴ or 625.

13. Answer :

=  5^1+x/5^x-1

=  5^(1+x)-(1+x)

=  5^1+x-1-x

=  5²

So, the answer is 25.

14. Answer :

=  8^x/16^y

8  =  2³ and 16  =  2⁴

=  2^3x/2^4y

=  2^3x-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 :

3^x-2  =  1/3²

3^x-2  =  1⋅3^-2

3^x-2  =  3^-2

x-2  =  -2

x  =  -2+2

x  =  0

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