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Indices
Algebraic Fractions
Surds
Quadratics
Mixed Bag
100

Evaluate 

8^(1/3)

without the use of a calculator

= 2

100

Simplify 

((a^5)^4 b^7)/(a^9 b)

=b^6/a^11

100

Rationalise the denominator of 

2/(5sqrt(3))

= (2sqrt(3))/15

100

Expand and simplify 

2(h+4)+3(2h-9)

=8h-19

100

Expand and simplify 

4ab(a-2b)-2a^2(b-3a)

= 2a(3a^2+ab-4b^2)

200

Rewrite 

xsqrt(x) 

in index form.

= x^(3/2)

200

Simplify 

(5a^9b^4c^-2) / (20a^5b^-3c^-1)

= (a^4b^7)/(4c)

200

Expand and simplify 

(2sqrt(6)+sqrt(5))(2sqrt(6)- sqrt(5))

=19

200

Expand and simplify 

(4n-3)(4n+3)-2n^2+5

=14n^2-4

200

If 

s=u+1/2at^2

find the exact value of s when 

u=sqrt(2), a=sqrt(3), t=2sqrt(3)

= sqrt(2) + 6sqrt(3)

300

Rewrite

z^(-3/4)

without fractional or negative indices

1/root(4)(z^3)

300

Fully simplify 

(5m+10)/(m^2-m-2) -: (m^2 -4)/(3m+3)

=15/(m-2)^2

300

Evaluate n if 

sqrt(108) - sqrt(12) = 4sqrt(n)

n = 3

300

Factorise 

(x+2)^2 - (2y-1)^2

=(x-2y+3)(x+2y+2)

300

Factorise 

4/x^2 - a^2/b^2

= ((2b-ax)(2b+ax))/((xb)^2)

400

Rewrite 

1/(root(3)((y+7)^2)

in index form.

= (y+7)^(-2/3)

400

Fully simplify 

(2xy+2x-6-6y)/(4x^2-16x+12)

= (y+1)/(2(x-1))

400

Rationalise the denominator of 

1/(2sqrt(5) - sqrt(3)

= (2sqrt(5)+sqrt(3))/17

400

Factorise 

19pq^2-15ypq+19rsq-15yrs

= (19q-15y)(pq+rs)

400

Simplify 

4/(k^2+2k-3) + 1/(k+3)

= 1/(k-1)