A serving of 100 g of powdered milk A provides 2120 KJ of energy.
(a) Express this amount of energy in standard form. Give your answer in Joules.

(b) Calculate the amount of energy, in Joules, that can be obtained from 2 kg of powdered milk A. Give your answer in Joules.

(c) A serving of 100 g of powdered milk B provides $9.78\times {10}^2$ KJ of energy.
Calculate the difference, in Joules, between the amount of energy obtained from powdered milk A and B in serving of 300 g.
Leave your answer in standard form.

A rectangular painting measures $4.5\times {10}^3$ mm by $3\times {10}^2$ mm.
Calculate, giving your answer in standard form:
(a) The perimeter of the painting,

(b) The area of the painting.

${(2\sqrt{5}\times \sqrt{20})}^{\frac{1}{2}}$

The diameter of the sun is approximately $1.39\times {10}^6$ km.
The diameter of the earth is approximately $1.27\times {10}^4$ km.
Leaving your answer in standard form, work out:
(a) The radius of the sun,

(b) By how many kilometres the diameter of the sun is greater than that of the earth.

Work out:
(a) $-2^3-9\times 4÷(2\times 3^2)$

(b) $4^{-\frac{1}{2}}+{16}^{\frac{3}{4}}$

Simplify:
(a) ${(m-2)}^2+(m^2-3)$

(b) $\frac{2^{x+1}-2^{x-1}}{2^x}$

Simplify $a^2\times a^{-3}-a^0$.

Evaluate the following:
(a) $4^0+4^{\frac{1}{2}}+4^2$

(b) ${27}^{-\frac{2}{3}}$

Work out:
(a) $7^0-6\times 2^2$,

(b) $8.4\times {10}^6-1.2\times {10}^5$,

(c) $\sqrt{169}-{0.64}^{0.5}$,

(d) $\sqrt[3]{2^9}$.

(a) Show that a − 2 + b 1 2 − 1 ( a b ) − 2 can be simplified to a 2 + b 2.

(b) Find the value of n in the following expression:
( 2 3 ) − 3 × ( 3 2 ) n = 1

(a) Evaluate $\frac{{\left(5\frac{1}{3}\right)}^2}{{(1-\frac{1}{3})}^3}$.

(b) Simplify $12{(-pt)}^2\times \frac{\sqrt{p^4{t}^2}}{3}\times {\left(\frac{p}{2t}\right)}^3$.

(a) Simplify $\frac{3^{x+3}-3^{x+1}}{3^{x+1}}$.

(b) Simplify $\frac{15p^3{q}^2}{12p^2{q}^3}$.