Question

1. Evaluate
[(1/4)^-3 - (1/3)^-3] ÷(1/6)^-3​

Answer 1

SOLUTION:

$\implies \bf \: \bigg[ \bigg( \frac{1}{4} \bigg)^{ - 3} \: - \: \bigg( \frac{1}{3} \bigg) ^{ - 3} \bigg] \: \div \bigg ( \frac{1}{6} \bigg) ^{ - 3} \\ \\ \implies \: \bf \: \bigg( \frac{4}{1} \bigg) ^{3} - \bigg( \frac{3}{1} \bigg) ^{3} \div \bigg( \frac{6}{1} \bigg) ^{3} \\ \\ \implies \bf \: 64 - 27 \div 216 \\ \\ \implies \: \bf \: 64 - (27 \times \frac{1}{216} ) \\ \\ \implies \bf \: 64 - \frac{1}{8} \\ \\ \implies \bf \: \frac{512}{8} - \frac{1}{8} \\ \\ \implies \: \bf \frac{511}{8}$