Simplify.
(a) $(w^3)^{10}$
(b) $t^6 v^7 \times t^3 v^{-2}$
Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):
(a)
When raising a power to another power, you simply multiply the exponents: $3 \times 10 = 30$.
✅ Answer: $w^{30}$
(b)
When multiplying terms with the same base, you add their exponents.
For $t$: $6 + 3 = 9$. For $v$: $7 + (-2) = 5$.
✅ Answer: $t^9 v^5$
(a) Work out \(48\div 3-5\times 2\).
(b) Insert one pair of brackets to make this statement correct.
3 + 2 × 12 – 4 = 19
(c) Write the following in order, starting with the smallest.
\(\frac{3}{4}\) 0.749 76%
(d) Find the value of [1 each]
(i) \(\sqrt{265.69}\)
(ii) 83
(e) Write down the smallest prime number.
(f) Write down all the factors of 18.
(g) Write down a common factor of 16 and 72 that is greater than 2.
(h) Write \(\frac{28}{140}\) as a fraction in its simplest form.
(i) Jeff and his friends win a prize.
Jeff’s share is $160 which is \(\frac{5}{11}\) of the prize.
Work out the value of the prize.
(a) Ans: 6
Using BIDMAS/BODMAS rules:
48 ÷ 3 = 16
5 × 2 = 10
16 – 10 = 6
(b) Ans: 3 + 2 × (12 – 4) = 19
Calculation:
12 – 4 = 8
2 × 8 = 16
3 + 16 = 19
(c) Ans: 0.749, \(\frac{3}{4}\), 76%
Convert all to decimals:
\(\frac{3}{4}\) = 0.75
76% = 0.76
Order: 0.749, 0.75, 0.76
(d)
(i) Ans: 16.3 (since 16.3 × 16.3 = 265.69)
(ii) Ans: 512 (8 × 8 × 8)
(e) Ans: 2
2 is the smallest and only even prime number
(f) Ans: 1, 2, 3, 6, 9, 18
Numbers that divide exactly into 18
(g) Ans: 4 or 8
Common factors of 16 (1,2,4,8,16) and 72 (1,2,3,4,6,8,9,12,18,24,36,72) >2
(h) Ans: \(\frac{1}{5}\)
Simplify by dividing numerator and denominator by 28
(i) Ans: $352
Let P = prize value
\(\frac{5}{11}\)P = 160 → P = 160 × \(\frac{11}{5}\) = 352
