Answer:
1. [tex]27^{\frac{2}{3} } =9[/tex]
2. [tex]\sqrt{36^{3} } =216[/tex]
3. [tex](-243)^{\frac{3}{5} } =-27[/tex]
4. [tex]40^{\frac{2}{3}}=4\sqrt[3]{25} =4325[/tex]
5. Step 4: [tex](\frac{343}{27}) ^{-1} =\frac{27}{343}[/tex]
6. [tex]D. -72cd^{7}[/tex]
Step-by-step explanation:
Use the following properties:
[tex]a^{\frac{x}{y} } =\sqrt[x]{a^{y} }[/tex]
[tex]\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}[/tex]
[tex]a^{-n} =\frac{1}{a^{n} }[/tex]
[tex](xy)^{z} =x^{z} y^{z} \\\\[/tex]
[tex](x^{y}) ^{z} =x^{yz}[/tex]
[tex]x^{y} x^{z} =x^{y+z}[/tex]
So:
1. [tex]27^{\frac{2}{3} } =\sqrt[3]{27^{2}} =\sqrt[3]{729} }=9[/tex]
2. [tex]\sqrt{36^{3} } =\sqrt{36*36*36} =\sqrt{36} \sqrt{36} \sqrt{36} =6*6*6=216[/tex]
3. [tex](-243)^{\frac{3}{5} } =\sqrt[5]{-243^{3} } =\sqrt[5]{-14348907} =-27[/tex]
4. [tex]40^{\frac{2}{3}}=\sqrt[3]{40^{2} } =\sqrt[3]{2^{6} 5^{2} } =\sqrt[3]{2^{6} } \sqrt[3]{5^{2} } =2^{\frac{6}{3} } 5^{\frac{2}{3} } =4 *5^{\frac{2}{3} } =4\sqrt[3]{5^{2} } =4\sqrt[3]{25}=4325[/tex]
5. [tex](\frac{343}{27}) ^{-1} =\frac{1}{\frac{343}{27} } =\frac{27}{343}[/tex]
6.
[tex](-8c^{9} d^{-3} )^{\frac{1}{3} } *(6c^{-1}d^{4})^{2} =\sqrt[3]{-8} c^{3} d^{-1} 36c^{-2} d^{8} \\\\-2c^{3} d^{-1} 36c^{-2} d^{8}=-72cd^{7}[/tex]
