Sievennä
a) \(a^2 \cdot a^6\)
b) \(\dfrac{a^2 \cdot a^7}{a^5}\)
c) \((b^3)^3\)
d) \(-2 \sqrt{3}+6 \sqrt{3}-9 \sqrt{3}\)
e) \(-5 \sqrt{5}+8 \sqrt{6}- \Big(-3 \sqrt{5}+2 \sqrt{6} \Big)\)
f) \(2 \sqrt{9}-2 \sqrt[3]{-27}+\sqrt{49}\)
Merkitse vihkoosi värikynällä pisteesi ja puuttuvat välivaiheet.
\(\require{cancel}\require{color} \begin{align*} \textbf{b)} \quad &\dfrac{a^2 \cdot a^7}{a^5} \\ =& \dfrac{\overbrace{\cancel{a}\cdot \cancel{a}}^{\text{2 kpl}} \cdot \overbrace{\cancel{a} \cdot \cancel{a} \cdot \cancel{a} \cdot a \cdot a \cdot a \cdot a}^{\text{7 kpl}}}{\underbrace{\cancel{a} \cdot \cancel{a} \cdot \cancel{a} \cdot \cancel{a} \cdot \cancel{a}}_{\text{5 kpl}} } \\ =&a^{9-5} =\underline{\underline{a^4}} \qquad \qquad\quad\color{red}\text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{c)} \quad &(b^3)^3 \\ =& \underbrace{b^3 \cdot b^3 \cdot b^3}_{\text{ 3 kpl}} \\ =& \underbrace{\underbrace{b \cdot b \cdot b}_{\text{3 kpl}} \cdot \underbrace{b \cdot b \cdot b}_{\text{3 kpl}} \cdot \underbrace{b \cdot b \cdot b}_{\text{3 kpl}}}_{3 \cdot 3\text{ kpl}} \\ =&b^{3 \cdot 3} =\underline{\underline{b^9}} \qquad \color{red}\text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{d)} \quad & -2 \sqrt{3}+6 \sqrt{3}-9 \sqrt{3} \\ =&\underline{\underline{-5 \sqrt{3}}} \qquad\qquad \color{red} \text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{e)}\quad & -5 \sqrt{5}+8 \sqrt{6}- \left(-3 \sqrt{5} +2 \sqrt{6} \right) \\ =&-5 \sqrt{5}+8 \sqrt{6}+3 \sqrt{5}-2 \sqrt{6} \\ =&\underline{\underline{-2 \sqrt{5}+6 \sqrt{6}}} \qquad \quad\color{red} \text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{f) }\quad &2 \sqrt{9}-2 \sqrt[3]{-27}+\sqrt{49} \\ =&2 \cdot 3 - 2 \cdot (-3) + 7 \\ =&6+6+7 \\ =&\underline{\underline{\ 19\ }} \qquad\qquad\qquad\color{red} \text{(+1p)} \end{align*}\)