The mass of a molecule of penicillin is \(10^{-18}\) kilogram and the mass of a molecule of insulin is \(10^{-23}\) kilogram. How many times greater is the mass of a molecule of penicillin than the mass of a molecule of insulin?

Justify Conclusions A common flea that is \(2^{-4}\) inch long can jump about \(2^{3}\) inches high. About how many times its body size can a flea jump? Explain your reasoning.

Identify Structure Without evaluating, order \(11^{-3}\), \(11^{2}\), and \(11^{0}\) from least to greatest. Explain your reasoning.

Identify Structure Write an expression with a negative exponent that has a value between 0 and \(\cfrac{1}{2}\).

Persevere with Problems Select several fractions between 0 and 1. Find the value of each fraction after it is raised to the -1 power. Explain the relationship between the -1 power and the original fraction.

Reason Abstractly For each power, write an equivalent multiplication expression with two factors. The first factor should have a positive exponent and the second factor should have a negative exponent.

a. \(10^{4} =\)

b. \(8^{2} =\)

c. \(\text{x}^{7} =\)