Question

A kilobyte is two raised to the tenth power bytes. A megabyte is two raised to the twentieth power bytes. How many kilobytes are in a megabyte?

two raised to the negative tenth power

two raised to the second power

two raised to the tenth power

two raised to the twentieth power

Answer 1

\[\large 1 \;Kb=2^{10}\;b \qquad \qquad \qquad 1\;Mb=2^{20}\;b\]

Lemme see if this works or not, writing the kilobytes as a proportion.\[\large 1\;Mb=\left(2^{20}b\right)\left(\frac{1\;Kb}{2^{10}\;b}\right)\]We put bytes on the bottom so we can cancel them out,\[\large 1\;Mb=\left(2^{20}\cancel b\right)\left(\frac{1\;Kb}{2^{10}\;\cancel b}\right)\]Giving us,\[\large 1\;Mb=\frac{2^{20}}{2^{10}}\;Kb\]

Answer 2

Recall that when we divide terms with similar bases, we `subtract` the exponents.\[\large 1\;Mb=2^{20-10}\;Kb\]