Find the value of \(\frac{5^{\frac{2}{3}}\times\sqrt[3]{5^7}}{\sqrt[3]{5^6}}\)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5
Write every term as a power of 5; then the powers are added when multiplying and subtracted when dividing.
\(\sqrt[3]{5^7}=5^{\frac{7}{3}}\) and \(\sqrt[3]{5^6}=5^{\frac{6}{3}}=5^2\)
Power of 5: \(\displaystyle \frac{2}{3}+\frac{7}{3}-2=3-2=1\)
The whole expression is therefore \(5^1=5\)