Structure and calculation：練習題

Which of the following mathematical statements is true?

Find the highest common factor (HCF) of 48 and 72.

Evaluate the expression \( \left( \frac{27}{8} \right)^{-\frac{2}{3}} \).

Calculate the following value using the correct order of operations:

\( 8 + 12 \div (6 - 2) \)

Calculate the value of the following expression using the priority of operations:

\( 5^2 - \sqrt{144} \div (7 - 4) \)

Using the correct order of operations, calculate the value of:
\(10 + 4 \times (3^2 - 5)\)

Using product notation, express 720 as a product of its prime factors.
Give your answer in index form.

Work out the exact value of \(\left( \frac{125}{64} \right)^{-\frac{2}{3}}\).
Give your answer as a fraction in its simplest form.

Calculate the following, showing your working at each step:

(a) \(4^3 - \sqrt{144}\)
(b) \(2 + 3 \times (10 - 2^2)\)

A rectangular playground has a length of \( 45.4 \text{ m} \) and a width of \( 28.7 \text{ m} \). Both measurements are given to the nearest 10 cm.

(a) Write down the lower bound and upper bound for the length of the playground.
(b) Calculate the upper bound for the area of the playground. Give your answer to 2 decimal places.