Index Laws I
Simplify 2a3 x 3a2
6a5
Simplify 3a0
3
Expand the following expression:
2t(t + 4)
2t2 + 8t
Factorise the following expression:
4n3 + 10n
2n(2n2 + 5)
Write the following number in scientific notation:
8 956 600 000
8.956 x 109
Is the following considered to be a surd?
sqrt3
Yes
Simplify the following expression
(3x^3)^2
9x6
Simplify the following expression:
5x-3
5/x^3
Expand the following expression:
(3x + 5)(x - 2)
3x2 - x - 10
Factorise the following expression:
6ab3 + 15ab
3ab(2b2 + 5)
Is the following number written in scientific notation?
73.6 x 10-8
No
Is the following number considered to be a surd?
sqrt18
No
Simplify the following expression
(m^2/4)^3
m^6/64
Simplify the following:
(3(x^2)^-2)/((3x)^3
1/(9x^7)
Expand and simplify the following expression:
7g2 + 4 - 3g(4g + 5)
4 - 15g
Factorise the following expression:
45fg5h4 - 36f2g4 +18fg2h
9fg2(5g3h4 - 4fg2 + 2h)
Write the following number in decimal form:
3.86 x 10-3
0.00386
Simplify the following
sqrt8
2sqrt2
Simplify the following expression:
(x^3y^4 * x^2y)/(x^8y^3
y^2/x^3
Simplify the following:
5x^0y + y(3x^4y^3)^0
6y
Expand and simplify the following expression:
(2x - 6y)(2x + 6y)
4x2 - 36y2
Factorise the following expression by grouping:
a2 + 3ab + 3ac + 9bc
(a + 3c)(a + 3b)
Without a calculator, evaluate (2 x 105) x (4 x 10-7). Leave your answer in scientific notation.
8 x 10-2
Simplify the following
sqrt27
3sqrt3
Simplify the following:
3(a^3b^4)^2*(2ab^2)^4
48a^10b^16
Simplify the following:
((4a)/b^2)^2 * ((3a^2)/(2b))^-2
64/(24a^2b^2)
Expand and simplify the following expression:
(4a + 5b)2
16a2 + 40ab + 25b2
Factorise the following expression by grouping:
12p3 - 21p2 + 28p - 49
(4p - 7)(3p2 + 7)
The land size of a country is approximately 110 600 square meters and its population is approximately 16 million. Determine the number of square meters per person living in this country, giving your answer in scientific notation.
6.91 x 10-3 m2 per person
Simplify the following
sqrt126
3sqrt14