Question

Which expression is equivalent to 3√64ab²c³?
2abc²[√4a²b³c]
4a²b²c³ (3√5)
8a³b³c¹ (3√/bc)
8a²b²c³(3√/b)

Answer 1

Answer:

$4a^2b^2c^3\left(\sqrt[3]{b}\right)$

Step-by-step explanation:

**Please note that the expression quoted in the question is likely incorrect (see attachment)**

Assuming the expression is:

$\sqrt[3]{64a^6b^7c^9}$

$\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}{ \cdot \sqrt{b}$

$\implies \sqrt[3]{64} \cdot \sqrt[3]{a^6}\cdot \sqrt[3]{b^7}\cdot \sqrt[3]{c^9}$

Rewrite 64 as 4³:

$\implies \sqrt[3]{4^3} \cdot \sqrt[3]{a^6}\cdot \sqrt[3]{b^7}\cdot \sqrt[3]{c^9}$

$\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \sf to\:\:b^7$

$\implies b^7=b^{6+1}=b^6b^1=b^6b$

Therefore:

$\implies \sqrt[3]{4^3} \cdot \sqrt[3]{a^6}\cdot \sqrt[3]{b^{6}b}\cdot \sqrt[3]{c^9}$

$\implies \sqrt[3]{4^3} \cdot \sqrt[3]{a^6}\cdot \sqrt[3]{b^{6}}\cdot \sqrt[3]{b}\cdot \sqrt[3]{c^9}$

$\textsf{Apply exponent rule} \quad \sqrt[n]{a^m}=a^{\frac{m}{n}}$

$\implies 4^{\frac{3}{3}} \cdot a^{\frac{6}{3}} \cdot b^{\frac{6}{3}} \cdot \sqrt[3]{b} \cdot c^{\frac{9}{3}}$

Simplify:

$\implies 4^1 \cdot a^2 \cdot b^2 \cdot \sqrt[3]{b} \cdot c^3$

$\implies 4a^2b^2c^3\left(\sqrt[3]{b}\right)$

Answer 2

• ³√64ab²c³
• √4³ab²c³
• 4c√a^{2/3}b^{2/3}

The expression is seemed to have none of the above solutions