Question

Find the value of:
a) (3/2)^(33)÷(2/3)^(-35)

Answer 1

Step-by-step explanation:

$(\frac{3}{2} ) {}^{33} \div (\frac{2}{3} ) {}^{ - 35} \\ \\ \\ = (\frac{3}{2} ) {}^{33} \div \frac{1}{ (\frac{2}{3}) {}^{ - ( - 35)} } \\ \\ \\ = ( \frac{3}{2}) {}^{33} \div (\frac{3}{2} ) {}^{35} \\ \\ \\ = (\frac{3}{2} ) {}^{(33 - 35)} \\ \\ \\ = ( \frac{3}{2} ) {}^{ - 2} \\ \\ \\ \\ formula \: \: \: - \: \: \: \: x {}^{ - 1} = \frac{1}{x} \\ \\ \\ x{}^{m} \div x {}^{n} = x {}^{m - n}$