Question

movement of the progress bar may be uneven because questions can be worth more or less (including zero) dependingMatch each expression on the left with an equivalent expression on the right.√64a5 b6-4a²b√√a-√64ab54ab²a²-64a7b³-8|a³|b² √b

Answer 1

Step-by-step explanation

let's remember some properties of the exponents and roots

`\begin{gathered} √(ab)=√(a)*√(b) \\ \sqrt[n]{a}\text{ = }a^{(1)/(n)} \\ \sqrt[n]{a^m}\text{ = }a^{(m)/(n)} \\ a^(m+n)=a^m*a^n \end{gathered}`

so

Step 1

given the first expression on the left

`\begin{gathered} \sqrt[3]{64a^5b^6} \\ hence \\ \sqrt[3]{64a^5b^6\text{ }}\text{ =}\sqrt[3]{64}\sqrt[3]{a^5}\text{ }\sqrt[3]{b^6}=4√(a^3a^2)\sqrt[3]{(b^2)^3}=4a\sqrt[3]{a^2}*b^2 \\ so \\ \sqrt[3]{64a^5b^6}\text{ =4ab}^2\sqrt[3]{a^2}^ \end{gathered}`

Step 2

second expression

`\begin{gathered} -√(64a^6b^5) \\ hence \\ -(\sqrt[]{64}\sqrt[]{a^6}\text{ }\sqrt[]{b^5})=-(4a^3√(b^4b)\text{ \rparen=-}(4a^3b^2√(b)) \end{gathered}`

so, the full answer is

I hope this helps you