Negative Index (Write without negative indices
Fractional Index
Simplifying Surds
Surds Arithmetic
Mystery
100

3^0

1

100

Write as a surd 

x^(4/5)\times 4 x^(5/7)

4x^(4/7)

100

\sqrt40 

2\sqrt10

100

(sqrt5)^2

5

100

(5x)/5

x

200

xy^-1

x/y

200

Write as fractional index

\sqrt(81x^5

9x^(5/2)

200

3\sqrt8

6\sqrt2

200

\sqrt6\times \sqrt10

2\sqrt15

200

5/a\div 10

1/(2a)

300

2x^-2\times 3x^-1

6x^-3

6/x^3

300

Rewrite with fractional and negative indices

-4/\sqrt(x^3)

-4x^(-3/2)

300

5\sqrt7-3\sqrt7

2\sqrt7

300

(3\sqrt10)/\sqrt5

3\sqrt2

300

a/(ax+ay)

1/(x+y)

400

(2m^4n^-2)^4

16m^16n^-8

16m^16/n^8

400

Write in surds

(x^(3/4))^4\times (x^(4/3))^3

x^7

400

7\sqrt6+5\sqrt3-4\sqrt6-7\sqrt3

3\sqrt6-2sqrt3

400

\sqrt6(\sqrt8-1)

\sqrt48-2\sqrt2

4\sqrt3-\sqrt6

400

Simplify FULLY

\sqrt40/\sqrt10

2

500

(10x^2y^-2)^3\div(2x^-1y^3)^2

250x^8y^-12

250x^8/y^12

500

5a^(1/3)b^(2/3)\times 7a^(-1/3)b^(1/3)

35b

500

\sqrt27+\sqrt75-\sqrt48

4 \sqrt3

500

(\sqrt6-1)(\sqrt6+1)

5

500

2\sqrt150-3\sqrt24=\sqrtx

x=96