https://peda.net/id/7c9581a2383 2020-01-16T10:09:15+02:00 https://peda.net/:static/535/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/1b963bf0384 2020-01-16T11:41:18+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%5B4%5D%7B81%7D%3D%5Csqrt%5B4%5D%7B3%5E4%7D%3D3" alt="\sqrt[4]{81}=\sqrt[4]{3^4}=3"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%5B6%5D%7B27%7D%3D%5Csqrt%5B6%5D%7B3%5E3%7D%3D3%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D" alt="\sqrt[6]{27}=\sqrt[6]{3^3}=3^{\frac{1}{2}}"/><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%5B6%5D%7B9%7D%3D%5Csqrt%5B6%5D%7B3%5E2%7D%3D3%5E%7B%5Cfrac%7B2%7D%7B6%7D%7D%3D3%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="\sqrt[6]{9}=\sqrt[6]{3^2}=3^{\frac{2}{6}}=3^{\frac{1}{3}}"/><br/> d)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B%5Csqrt%5B3%5D%7B9%7D%7D%7B%5Csqrt%7B3%7D%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%5Ccdot%5Csqrt%5B3%5D%7B3%5E2%7D%3D3%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%5Ccdot3%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%3D3%5E%7B-%5Cfrac%7B3%7D%7B6%7D%7D%5Ccdot3%5E%7B%5Cfrac%7B4%7D%7B6%7D%7D%3D3%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D" alt="\frac{\sqrt[3]{9}}{\sqrt{3}}=\frac{1}{\sqrt{3}}\cdot\sqrt[3]{3^2}=3^{-\frac{1}{2}}\cdot3^{\frac{2}{3}}=3^{-\frac{3}{6}}\cdot3^{\frac{4}{6}}=3^{\frac{1}{6}}"/> 2020-01-16T11:39:35+02:00 https://peda.net/id/18848490384 2020-01-16T11:32:21+02:00 <div>a)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B32%7D%3D%5Csqrt%7B2%5E5%7D%3D2%5E%7B%5Cfrac%7B5%7D%7B2%7D%7D" alt="\sqrt{32}=\sqrt{2^5}=2^{\frac{5}{2}}"/></div> <div>b)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%5B5%5D%7B16%7D%3D%5Csqrt%5B5%5D%7B2%5E4%7D%3D2%5E%7B%5Cfrac%7B4%7D%7B5%7D%7D" alt="\sqrt[5]{16}=\sqrt[5]{2^4}=2^{\frac{4}{5}}"/></div> <div>c)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B%5Csqrt%5B3%5D%7B4%7D%7D%3D%5Csqrt%7B%5Csqrt%5B3%5D%7B2%5E2%7D%7D%3D2%5E%7B%5Cfrac%7B2%7D%7B6%7D%7D%3D2%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="\sqrt{\sqrt[3]{4}}=\sqrt{\sqrt[3]{2^2}}=2^{\frac{2}{6}}=2^{\frac{1}{3}}"/></div> <div>d)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B%5Csqrt%5B3%5D%7B16%7D%7D%7B%5Csqrt%7B2%7D%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%5Ccdot%5Csqrt%5B3%5D%7B2%5E4%7D%3D2%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%5Ccdot2%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%3D2%5E%7B-%5Cfrac%7B3%7D%7B6%7D%7D2%5E%7B%5Cfrac%7B8%7D%7B6%7D%7D%3D2%5E%7B%5Cfrac%7B5%7D%7B6%7D%7D" alt="\frac{\sqrt[3]{16}}{\sqrt{2}}=\frac{1}{\sqrt{2}}\cdot\sqrt[3]{2^4}=2^{-\frac{1}{2}}\cdot2^{\frac{4}{3}}=2^{-\frac{3}{6}}2^{\frac{8}{6}}=2^{\frac{5}{6}}"/></div> 2020-01-16T11:32:21+02:00 https://peda.net/id/04ebfc20384 2020-01-16T11:24:38+02:00 a)<br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=4%5E%7B1%7B%2C%7D5%7D%3D4%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%3D%5Csqrt%7B4%5E3%7D%3D%5Csqrt%7B4%5E2%7D%5Csqrt%7B4%7D%3D4%5Csqrt%7B4%7D" alt="4^{1{,}5}=4^{\frac{3}{2}}=\sqrt{4^3}=\sqrt{4^2}\sqrt{4}=4\sqrt{4}"/></div> <div>b)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=4%5E%7B0%7B%2C%7D75%7D%3D4%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D%5Csqrt%5B4%5D%7B4%5E3%7D%3D%5Csqrt%5B4%5D%7B2%5E6%7D%3D%5Csqrt%5B4%5D%7B2%5E4%7D%5Csqrt%5B4%5D%7B2%5E2%7D%3D2%5Csqrt%5B4%5D%7B4%7D" alt="4^{0{,}75}=4^{\frac{3}{4}}=\sqrt[4]{4^3}=\sqrt[4]{2^6}=\sqrt[4]{2^4}\sqrt[4]{2^2}=2\sqrt[4]{4}"/></div> <div>c)</div> <div> </div> <img src="https://math-demo.abitti.fi/math.svg?latex=27%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%3D%5Csqrt%5B3%5D%7B27%5E2%7D%3D%5Csqrt%5B3%5D%7B3%5E6%7D%3D3%5E%7B%5Cfrac%7B6%7D%7B3%7D%7D%3D3%5E2%3D9" alt="27^{\frac{2}{3}}=\sqrt[3]{27^2}=\sqrt[3]{3^6}=3^{\frac{6}{3}}=3^2=9"/><br/> <div>d)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=25%5E%7B-%5Cfrac%7B3%7D%7B2%7D%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B25%5E3%7D%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B5%5E6%7D%7D%3D5%5E%7B-%5Cfrac%7B6%7D%7B2%7D%7D%3D5%5E%7B-3%7D%3D%5Cfrac%7B1%7D%7B125%7D" alt="25^{-\frac{3}{2}}=\frac{1}{\sqrt{25^3}}=\frac{1}{\sqrt{5^6}}=5^{-\frac{6}{2}}=5^{-3}=\frac{1}{125}"/></div> 2020-01-16T11:24:38+02:00 https://peda.net/id/2895d67a384 2020-01-16T11:11:19+02:00 a) <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B2a%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D%7B3%7D%3D%5Cfrac%7B2%5Csqrt%5B3%5D%7Ba%7D%7D%7B3%7D" alt="\frac{2a^{\frac{1}{3}}}{3}=\frac{2\sqrt[3]{a}}{3}"/></div> <div>b)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=6a%5E%7B%5Cfrac%7B5%7D%7B2%7D%7D%3D6%5Csqrt%7Ba%5E5%7D" alt="6a^{\frac{5}{2}}=6\sqrt{a^5}"/></div> <div>c)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=7a%5E%7B-%5Cfrac%7B4%7D%7B5%7D%7D%3D%5Cfrac%7B7%7D%7B%5Csqrt%5B5%5D%7Ba%5E4%7D%7D" alt="7a^{-\frac{4}{5}}=\frac{7}{\sqrt[5]{a^4}}"/></div> <div>d)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7Ba%5E%7B-%5Cfrac%7B9%7D%7B5%7D%7D%7D%7B4%7D%3D%5Cfrac%7B1%7D%7B4%5Csqrt%5B5%5D%7Ba%5E9%7D%7D" alt="\frac{a^{-\frac{9}{5}}}{4}=\frac{1}{4\sqrt[5]{a^9}}"/></div> 2020-01-16T11:11:19+02:00 https://peda.net/id/764eacc8383 2020-01-16T10:52:01+02:00 <div>162</div> <div>a)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B2%7D%7B%5Csqrt%7Bx%7D%7D%3D2%5Ccdot%5C%20%5Cfrac%7B1%7D%7B%5Csqrt%7Bx%7D%7D%3D2%5Csqrt%7Bx%5E%7B-1%7D%7D%3D2x%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D" alt="\frac{2}{\sqrt{x}}=2\cdot\ \frac{1}{\sqrt{x}}=2\sqrt{x^{-1}}=2x^{-\frac{1}{2}}"/></div> <div>b)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7Bx%5E2%7D%7B3%5Csqrt%7Bx%7D%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot%5Cfrac%7Bx%5E2%7D%7B%5Csqrt%7Bx%7D%7D%3D%5Cfrac%7B1%7D%7B3%7Dx%5E2%5Ccdot%20x%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Cfrac%7B1%7D%7B3%7Dx%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D" alt="\frac{x^2}{3\sqrt{x}}=\frac{1}{3}\cdot\frac{x^2}{\sqrt{x}}=\frac{1}{3}x^2\cdot x^{-\frac{1}{2}}=\frac{1}{3}x^{\frac{3}{2}}"/><br/> c)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B3%7D%7B4x%5Csqrt%7Bx%7D%7D%3D%5Cfrac%7B3%7D%7B4%7D%5Ccdot%5Cfrac%7B1%7D%7Bx%5Csqrt%7Bx%7D%7D%3D%5Cfrac%7B3%7D%7B4%7Dx%5E%7B-1%7Dx%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Cfrac%7B3%7D%7B2%7Dx%5E%7B-%5Cfrac%7B3%7D%7B2%7D%7D" alt="\frac{3}{4x\sqrt{x}}=\frac{3}{4}\cdot\frac{1}{x\sqrt{x}}=\frac{3}{4}x^{-1}x^{-\frac{1}{2}}=\frac{3}{2}x^{-\frac{3}{2}}"/></div> <div>d)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B2%5Csqrt%7Bx%7D%7D%7B5x%7D%3D%5Cfrac%7B2%7D%7B5%7D%5Ccdot%5Cfrac%7B%5Csqrt%7Bx%7D%7D%7Bx%7D%3D%5Cfrac%7B2%7D%7B5%7D%5Ccdot%20x%5E%7B-1%7D%5Ccdot%20x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Cfrac%7B2%7D%7B5%7Dx%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D" alt="\frac{2\sqrt{x}}{5x}=\frac{2}{5}\cdot\frac{\sqrt{x}}{x}=\frac{2}{5}\cdot x^{-1}\cdot x^{\frac{1}{2}}=\frac{2}{5}x^{-\frac{1}{2}}"/></div> <div> </div> 2020-01-16T10:52:01+02:00