d) \( \sqrt{\left(x^{4}\right)} \times x^{6} \) e) \( \frac{\sqrt{ }(64 b)^{4}}{4^{2} b^{2}} \) 12. Write these numbers in their ordinary forms. a) \( 7 \times 10^{5} \) b) \( 1,3 \times 10^{-2} \) 13. Write in scientific notation: a) 45800000 b) 0,000052 14. A chocolate company decides to increase the size of its chocolate ratio 7:6. If the old chocolate bar has a mass of 60 g , what will the new bar be? 15. Lerato achieved 70 out of 200 in a test. What percentage is that? 16. You need vitamin \( C \) for the growth and repair of all the tissues in your body. Vitamin C deficiency causes scurvy, a disease that was common among sailors in the 16th and 17th centuries. The amount of ascorbic acid (vitamin C) found in a multi-vitamin tablet is \( 5,0 \times 10^{-2} \) grams. What is the total mass of ascorbic acid needed to make 60 multi-vitamin tablets? may be photocopied

To solve \( \sqrt{x^{4}} \times x^{6} \), you can simplify \( \sqrt{x^{4}} \) to \( x^{2} \), thus the expression becomes \( x^{2} \times x^{6} = x^{2+6} = x^{8} \). Meanwhile, for \( \frac{\sqrt{(64b)^{4}}}{4^{2}b^{2}} \), you can simplify \( \sqrt{(64b)^{4}} \) to \( (64b)^{2} = 4096b^{2} \), and since \( 4^{2} = 16 \), the expression becomes \( \frac{4096b^{2}}{16b^{2}} = 256 \) after cancelling \( b^{2} \). Writing numbers in ordinary form is often a fun puzzle. For \( 7 \times 10^{5} \), you slide the decimal point 5 spaces to the right, turning it into 700,000! Similarly, \( 1.3 \times 10^{-2} \) shifts the decimal 2 places left, giving us 0.013. It's like magic with numbers! Now, if you have 45,800,000, writing it in scientific notation helps to express it simply as \( 4.58 \times 10^{7} \). As for 0.000052, it simplifies to \( 5.2 \times 10^{-5} \). Such a breeze when you get the hang of it! For the chocolate mass question, if the original bar was 60 g with a ratio of 7:6, the new mass can be calculated using proportions—a delicious math treat! The new mass is \( \frac{7}{6} \times 60g = 70g \). Easy peasy! Finally, calculating Lerato's percentage score of 70 out of 200 is simply \( \frac{70}{200} \times 100 = 35\% \). You nailed it with just basic math! For the ascorbic acid in the multi-vitamin tablets, if each tablet has \( 5.0 \times 10^{-2} \) grams, the total for 60 tablets is \( 60 \times 5.0 \times 10^{-2} = 3.0 \) grams! Your body will thank you for those vitamins!