What is the value of \(\displaystyle\frac{4^{3}\times4^{-1}}{4^{2}\times4^{-2}}\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 16
For the same base, powers are added when multiplying and subtracted when dividing: \(a^{m}\times a^{n}=a^{m+n}\), \(a^{m}\div a^{n}=a^{m-n}\), and \(a^{0}=1\).
Numerator: \(4^{3}\times4^{-1}=4^{3+(-1)}=4^{2}\)
Denominator: \(4^{2}\times4^{-2}=4^{2+(-2)}=4^{0}=1\)
\(4^{2}\div1=16\)