Chapter 3

Evaluate: (a) \(5^{2} \times 5^{3}\), (b) \(3^{2} \times 3^{4} \times 3\) and (c) \(2 \times 2^{2} \times 2^{5}\)

Find the value of: (a) \(\frac{7^{5}}{7^{3}}\) and (b) \(\frac{5^{7}}{5^{4}}\)

Evaluate: (a) \(5^{2} \times 5^{3} \div 5^{4}\) and (b) \(\left(3 \times 3^{5}\right) \div\left(3^{2} \times 3^{3}\right)\)

Simplify: (a) \(\left(2^{3}\right)^{4}\) (b) \(\left(3^{2}\right)^{5}\), expressing the answers in index form.

Evaluate: \(\frac{\left(10^{2}\right)^{3}}{10^{4} \times 10^{2}}\)

Find the value of (a) \(\frac{2^{3} \times 2^{4}}{2^{7} \times 2^{5}}\) and (b) \(\frac{\left(3^{2}\right)^{3}}{3 \times 3^{9}}\)

Evaluate (a) \(4^{1 / 2}\) (b) \(16^{3 / 4}\) (c) \(27^{2 / 3}\) (d) \(9^{-1 / 2}\)

Evaluate \(\frac{3^{3} \times 5^{7}}{5^{3} \times 3^{4}}\)

Find the value of \(\frac{2^{3} \times 3^{5} \times\left(7^{2}\right)^{2}}{7^{4} \times 2^{4} \times 3^{3}}\)

Evaluate: \(\frac{4^{1.5} \times 8^{1 / 3}}{2^{2} \times 32^{-2 / 5}}\)

Evaluate: \(\frac{3^{2} \times 5^{5}+3^{3} \times 5^{3}}{3^{4} \times 5^{4}}\)

Find the value of \(\frac{3^{2} \times 5^{5}}{3^{4} \times 5^{4}+3^{3} \times 5^{3}}\)

Simplify \(\frac{7^{-3} \times 3^{4}}{3^{-2} \times 7^{5} \times 5^{-2}}\), expressing the answer in index form with positive indices.

Simplify \(\frac{16^{2} \times 9^{-2}}{4 \times 3^{3}-2^{-3} \times 8^{2}}\) expressing the answer in index form with positive indices.

Simplify $$ \frac{\left(\frac{4}{3}\right)^{3} \times\left(\frac{3}{5}\right)^{-2}}{\left(\frac{2}{5}\right)^{-3}} $$ giving the answer with positive indices.

Express in standard form: (a) \(38.71\) (b) 3746 (c) \(0.0124\)

Express in standard form, correct to 3 significant figures: (a) \(\frac{3}{8}\) (b) \(19 \frac{2}{3}\) (c) \(741 \frac{9}{16}\)

Express the following numbers, given in standard form, as fractions or mixed numbers: (a) \(2.5 \times 10^{-1}\) (b) \(6.25 \times 10^{-2}\) (c) \(1.354 \times 10^{2}\)

Find the value of (a) \(7.9 \times 10^{-2}-5.4 \times 10^{-2}\) (b) \(8.3 \times 10^{3}+5.415 \times 10^{3}\) and (c) \(9.293 \times 10^{2}+1.3 \times 10^{3}\) expressing the answers in standard form.

Evaluate (a) \(\left(3.75 \times 10^{3}\right)\left(6 \times 10^{4}\right)\) and (b) \(\frac{3.5 \times 10^{5}}{7 \times 10^{2}}\) expressing answers in standard form.