Laske
a) \(3^3\)
b) \((-3)^4\)
c) \(-3^4\)
d) \(\sqrt{25}\)
e) \(\sqrt[3]{27}\)
f) \(5 \cdot (-2)^2 +(-3)^3\)
Merkitse vihkoosi värikynällä pisteesi ja puuttuvat välivaiheet.
\(\require{color} \begin{align*} \textbf{a)} \quad3^3 =\underbrace{3\cdot 3 \cdot 3}_{3 \text{kpl}} =\underline{\underline{\ 27\ }} \quad \color{red}{\text{(+1p)}} \end{align*}\)
\(\require{color} \begin{align*} \textbf{b)} \quad &(-3)^4 \\ =& \underbrace{(-3) \cdot (-3) \cdot (-3) \cdot (-3)}_{\text{ 4 kpl}}\\ =&\underline{\underline{81}} \qquad\qquad\qquad \color{red}{\text{(+1p)}} \end{align*}\)
\(\require{color} \begin{align*} \textbf{c)} \quad &-3^4 =-\underbrace{3 \cdot 3 \cdot 3 \cdot 3}_{\text{4 kpl}}\\ =&\underline{\underline{-81}} \qquad\qquad\qquad \color{red}{\text{(+1p)}} \end{align*}\)
\(\require{color} \begin{align*} \textbf{d)} &\sqrt{25}=\underline{\underline{\ 5\ }} \text{ (koska } 5^2=25) \quad \color{red}{\text{(+1p)}} \end{align*}\)
\(\require{color} \begin{align*} \textbf{e) } \sqrt[3]{27}=\underline{\underline{\ 3\ }} \text{ (koska } 3^3=27) \quad \color{red}{\text{(+1p)}} \end{align*}\)
\(\require{color} \begin{align*} \textbf{f)} \quad&5 \cdot (-2)^2 +(-3)^3 \\ =&5 \cdot (-2) \cdot (-2) + (-3) \cdot (-3) \cdot (-3) \\ =&20-27=\underline{\underline{-7}} \qquad \color{red}{\text{(+1p)}} \end{align*}\)
Sievennä
a) \(a^4 \cdot a^5\)
b) \(\dfrac{a^3 \cdot a^6}{a^7}\)
c) \((b^3)^2\)
d) \(4 \sqrt{4}+6 \sqrt{4}-2 \sqrt{4}\)
e) \(3 \sqrt{3}+2 \sqrt{4}- \Big(6 \sqrt{3}-5 \sqrt{4} \Big)\)
f) \(-2 \sqrt{4}+3 \sqrt[3]{8}+\sqrt{16}\)
Merkitse vihkoosi värikynällä pisteesi ja puuttuvat välivaiheet.
\(\require{cancel}\require{color} \begin{align*} \textbf{b)} \quad &\dfrac{a^3 \cdot a^6}{a^7} \\ =& \dfrac{\overbrace{\cancel{a}\cdot \cancel{a} \cdot \cancel{a}}^{\text{3 kpl}} \cdot \overbrace{\cancel{a} \cdot \cancel{a} \cdot \cancel{a} \cdot \cancel{a} \cdot a \cdot a}^{\text{6 kpl}}}{\underbrace{\cancel{a} \cdot \cancel{a} \cdot \cancel{a} \cdot \cancel{a} \cdot \cancel{a} \cdot \cancel{a} \cdot \cancel{a}}_{\text{7 kpl}} } \\ =&a^{9-7} =\underline{\underline{a^2}} \qquad \qquad\quad\color{red}\text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{c)} \quad &(b^3)^2\\ =& \underbrace{b^3 \cdot b^3}_{\text{ 2 kpl}} \\ =& \underbrace{\underbrace{b \cdot b \cdot b}_{\text{3 kpl}} \cdot \underbrace{b \cdot b \cdot b}_{\text{3 kpl}}}_{3 \cdot 2\text{ kpl}} \\ =&b^{3 \cdot 2} =\underline{\underline{b^6}} \qquad \color{red}\text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{d)} \quad & 4 \sqrt{4}+6 \sqrt{4}-2 \sqrt{4} \\ =&\underline{\underline{8 \sqrt{4}}} \qquad\qquad \color{red} \text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{e)}\quad & 3 \sqrt{3}+2 \sqrt{4}- \left(6 \sqrt{3}-5 \sqrt{4} \right)\\ =&3 \sqrt{3}+2 \sqrt{4}-6 \sqrt{3}+5 \sqrt{4} \\ =&\underline{\underline{-3 \sqrt{3}+7 \sqrt{4}}} \qquad \quad\color{red} \text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{f) }\quad &-2 \sqrt{4}+3 \sqrt[3]{8}+\sqrt{16}\\ =&-2 \cdot 2 + 3 \cdot 2 + 4 \\ =&-4+6+4 \\ =&\underline{\underline{\ 6\ }} \qquad\qquad\qquad\color{red} \text{(+1p)} \end{align*}\)
Laske
a) \(7-3^2\)
b) \((7-3)^2\)
c) \(\dfrac{16^3}{8^3}\)
d) \(0,2^4 \cdot 10^4\)
e) \(\sqrt{18} \cdot \sqrt{2}\)
f) \(\dfrac{\sqrt[3]{80}}{\sqrt[3]{10}}\)
Merkitse vihkoosi värikynällä pisteesi ja puuttuvat välivaiheet.
\(\require{color} \begin{align*} \textbf{a)}\quad &7-3^2\\ =&7-\underbrace{3 \cdot 3}_{\text{2 kpl}} \\ =&7-9 \\ =&\underline{\underline{-2}} && \color{red}\text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{b) }\quad & (7-3)^2 \\ =&4^2 \\ =&4 \cdot 4 \\ =&\underline{\underline{\ 16\ }} &&\color{red}\text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{c)}\quad & \dfrac{16^3}{8^3} && \Big|\Big| \Big(\dfrac{a}{b}\Big)^n=\dfrac{a^n}{b^n}\\ =&\Big(\dfrac{16}{8} \Big)^3 \\ =&2^3 \\ =&2 \cdot 2 \cdot 2 \\ =&\underline{\underline{\ 8\ }} && \color{red}\text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{d)} \quad &0,2^4 \cdot 10^4 && \Big| \Big| (a \cdot b)^n = a^n \cdot b^n \\ =&(0,2 \cdot 10)^4 \\ =&2^4 \\ =&2 \cdot 2 \cdot 2 \cdot 2 \\ =&\underline{\underline{16}} && \color{red}\text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{e)} \quad &\sqrt{18} \cdot \sqrt{2} \qquad \quad | | \sqrt[n]{a} \cdot \sqrt[n]{b}=\sqrt[n]{a \cdot b} \\ =&\sqrt{18 \cdot 2} \\ =&\sqrt{36} \\ =&\underline{\underline{\ 6\ }} \quad \text{ (koska } 6^2=36) \qquad \color{red}\text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{f)} \quad &\dfrac{\sqrt[3]{80}}{\sqrt[3]{10}} \qquad\qquad \Big| \Big| \dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\dfrac{a}{b}} \\ =&\sqrt[3]{\dfrac{80}{10}} \\ =&\sqrt[3]{8} \\ =&\underline{\underline{\ 2\ }} \text{ (koska } 2^3=8) \qquad \color{red}\text{(+1p)} \end{align*}\)
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