Question

2^5/2^3*4^-1/4^-2.
Evaluate. Leave all your answers as powers using positive exponents.

Answer 1

well the rule for division is subtract the powers

\[\frac{x^a}{x^b} = x^{a -b}\]

and the rule for multiplication is add the powers

\[x^a \times x^b = x^{a + b}\]

and lastly power of a power... multiply the powers

\[(x^a)^b = x^{a \times b}\]

you need all 3 for this question

and you need to write 4 as 2^2

so you have

\[\frac{2^5}{2^3} \times \frac{(2^2)^{-1}}{(2^2)^{-2}} = \frac{2^5 \times 2^{-2}}{2^3 \times 2^{-4}}\]

just just the rules above to simplify