Indices
Evaluate
8^(1/3)
without the use of a calculator
= 2
Simplify
((a^5)^4 b^7)/(a^9 b)
=b^6/a^11
Rationalise the denominator of
2/(5sqrt(3))
= (2sqrt(3))/15
Expand and simplify
2(h+4)+3(2h-9)
=8h-19
Expand and simplify
4ab(a-2b)-2a^2(b-3a)
= 2a(3a^2+ab-4b^2)
Rewrite
xsqrt(x)
in index form.
= x^(3/2)
Simplify
(5a^9b^4c^-2) / (20a^5b^-3c^-1)
= (a^4b^7)/(4c)
Expand and simplify
(2sqrt(6)+sqrt(5))(2sqrt(6)- sqrt(5))
=19
Expand and simplify
(4n-3)(4n+3)-2n^2+5
=14n^2-4
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)
Rewrite
z^(-3/4)
without fractional or negative indices
1/root(4)(z^3)
Fully simplify
(5m+10)/(m^2-m-2) -: (m^2 -4)/(3m+3)
=15/(m-2)^2
Evaluate n if
sqrt(108) - sqrt(12) = 4sqrt(n)
n = 3
Factorise
(x+2)^2 - (2y-1)^2
=(x-2y+3)(x+2y+2)
Factorise
4/x^2 - a^2/b^2
= ((2b-ax)(2b+ax))/((xb)^2)
Rewrite
1/(root(3)((y+7)^2)
in index form.
= (y+7)^(-2/3)
Fully simplify
(2xy+2x-6-6y)/(4x^2-16x+12)
= (y+1)/(2(x-1))
Rationalise the denominator of
1/(2sqrt(5) - sqrt(3)
= (2sqrt(5)+sqrt(3))/17
Factorise
19pq^2-15ypq+19rsq-15yrs
= (19q-15y)(pq+rs)
Simplify
4/(k^2+2k-3) + 1/(k+3)
= 1/(k-1)