Review and use the the rules for radicals and exponents to simplify exponents and radical expressions; questions with detailed solutions and explanations are presented along with their detailed solutions Try not to use the calculator to simplify numerical expressions except to check your answers. More questions on how to simplify radical expressions are included n this website.

## Evaluate Numerical Expressions with Exponents

### Question 1

Evaluate the following expressions:
1.   32
2.   - 34
3.   (- 3)4
4.   120
5.   020
6.   0- 4
7.   (-1)7
8.   (-1)4
9.   (-1) - 3
10.   (- 2 / 3) -2
11.   (- 2)-2 / 4-2
12.   - 3-3 + (- 2)-2
13.   x4 for x = - 2
14.   - x2 for x = - 3
15.   - x5 for x = - 2
16.   x4 for x = - 2 / 3
17.   - x-2 for x = - 1 / 2
18.   - x5 for x = - 1 / 3
detailed solutions

## Evaluate Numerical Expressions with Radicals and rational exponents

### Question 2

Evaluate the following expressions:
1.   √(64)
2.   ∛(-8)
3.   43/2
4.   82/3
5.   0.00013/4
6.   16- 3/4
7.   √2 √8
8.   ∛2 ∛(32)
9.   √2 / √8
10.   ∛(-16) / ∛2
11.   - 2 (6√8) (56√8)
12.   - 4 ∛(375) / (2∛3)
detailed solutions

## Simplify Algebraic Expressions with Exponents

### Question 3

Simplify the following expressions:
1.   x2 x5
2.   y4 / y2
3.   (x2)-2

4. \large {3(\dfrac{1}{2} x^4)(\dfrac{1}{3} x^3) }

5. \large {(2 x)^4(\dfrac{1}{4} x^{-3}) }

6. \large { \dfrac{(3x)^2(-2x)^3}{(2x)^2} }

7. \large { \dfrac{(4x)^2(100 x)^0}{(3x)^2} }
8.   (- 2 x2 y -3)3
9.   (3 x2 y3) (2 x5 y - 2)
10.   (- 2 x2 y3 z4) ( - 4 x3 y z - 8) ( 5 x y2 z2)

11. \large { (-2xy^2)^2 \left (\dfrac{x^6}{(2x)^2} \right)^3 }

12. \large { \left (\dfrac{4 x^6 y^3}{-8x^3y^{-2}} \right) }

13. \large { \left (\dfrac{- 4 x^3 y^2}{3 x^3 y^3} \right) \left (\dfrac{3 x^2 y^5}{-6x^3y^2} \right) }

14. \large { \dfrac{1}{6}(x^2 y z^3)\left (\dfrac{4 x^2 y^3}{3 x^2 y^{-3}z^2} \right) \left (\dfrac{3 x^2 y^5 z}{-x^3 y^2 z^3} \right) }

15. \large { (4 x^{2/3})(-8x^{1/2}) }

16. \large { (4 x)^{3/2}(9x)^{1/2} }

17. \large { (- 27 x^{3/2})^{1/3} }

18. \large {\left (\dfrac{-8x^3}{y^{-6}} \right)^{2/3} }

19. \large { x^{5/3} x^{1/6} x ^{-11/6} }
detailed solutions

## Simplify Algebraic Expressions with Radicals

### Question 4

1. \large { \sqrt{x^2} }

2. \large { \sqrt[4]{16x^4} }

3. \large { \sqrt{(2x - 1)^2} }

4. \large { \sqrt[3]{-27x^3} }

5. \large { \sqrt[3]{8 x^6 y^3} }

6. \large { \sqrt{x^3} \sqrt{x^2} }

7. \large { \sqrt[3]{\left (\dfrac{-8x^6}{y^{-3}} \right)} y}

8. \large { \dfrac{ \sqrt[5]{64x^9 y^7}}{ \sqrt[5]{2 x^4 y^2}} }

9. \large { (4\sqrt[8]{b^2})( 5\sqrt[8]{b^3})( \sqrt[8]{b^3}) }
detailed solutions