Question

[tex] \sqrt[3]{625} \times {25}^{ \frac{3}{4} } \times \sqrt[6]{5} \ \\ \ {125}^{? \times \frac{2}{3} } \div {5}^{ - 3} [/tex]
byłabym mega wdzięczna
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Answer 1

Verified answer

[tex]\dfrac{\sqrt[3]{625}\cdot25^{\frac{3}{4}}\cdot\sqrt[6]{5}}{125^{\frac{2}{3}}:5^{-3}}=\dfrac{625^{\frac{1}{3}}\cdot25^{\frac{3}{4}}\cdot5^{\frac{1}{6}}}{((5^3)^{\frac{2}{3} }:5^{-3}}=\dfrac{(5^4)^{\frac{1}{3}}\cdot(5^2)^{\frac{3}{4}}\cdot5^{\frac{1}{6}}}{5^{3\cdot\frac{2}{3}}:5^{-3}}=\dfrac{5^{4\cdot\frac{1}{3}}\cdot5^{2\cdot\frac{3}{4}}\cdot5^{\frac{1}{6}}}{5^2:5^{-3}}=[/tex]

[tex]=\dfrac{5^{\frac{4}{3}}\cdot5^{\frac{3}{2}}\cdot5^{\frac{1}{6}}}{5^{2-(-3)}}=\dfrac{5^{\frac{4}{3}+\frac{3}{2}+\frac{1}{6}}}{5^{2+3}}=\dfrac{5^{\frac{8}{6}+\frac{9}{6}+\frac{1}{6}}}{5^5}=\dfrac{5^{\frac{18}{6}}}{5^5}=\dfrac{5^3}{5^5}=5^{3-5}=5^{-2}[/tex]

Odp. A

Zastosowane wzory

[tex]\sqrt[n]{a}=a^{\frac{1}{n}}\\\\(a^m)^n=a^{m\cdot n}\\\\a^m\cdot a^n=a^{m+n}\\\\a^m:a^n=a^{m-n}\\\\\frac{a^m}{a^n}=a^{m-n}\ \ \ \ \ \ dla\ \ a\neq 0[/tex]