$(a\cdot b)^n=a^n \cdot b^n$

Oppgave 1

  • \begin{align}(xy^2)^3=x^3\cdot y^{2\cdot 3}=x^3y^6\end{align}

  • \begin{align}(x^2 y)^2=x^{2\cdot 2}\cdot y^2=x^4y^2\end{align}

  • \begin{align}(a^2b^2c)^2=a^{2\cdot 2}\cdot b^{2\cdot 2}\cdot c^2=a^{4}b^{4}c^2\end{align}

  • \begin{align}
    (a^3b^2)^{-1}
    &=a^{3\cdot (-1)}\cdot b^{2\cdot (-1)}\\
    &=\frac{1}{a^3b^2}
    \end{align}

Oppgave 2

  • Løsningsforslag:
    \begin{align}(a^2)^{-3}
    &=a^{2\cdot (-3)}\\
    &=a^{-6}\\
    &=\frac{1}{a^6}
    \end{align}

  • \begin{align}
    (x^2)^7
    &=x^{2\cdot 7}\\
    &=x^{2\cdot 7}\\
    &=x^{14}
    \end{align}

  • \begin{align}
    (a^2)^3
    &=a^{2\cdot 3}\\
    &=a^6
    \end{align}

  • \begin{align}
    (b^2)^{-1}
    &=b^{2\cdot (-1)}\\
    &=b^{-2}\\
    &=\frac{1}{b^2}
    \end{align}

Oppgave 3

  • \begin{align}
    (x^2)^3
    &=x^{2\cdot 3}\\
    &=x^6
    \end{align}

  • \begin{align}
    (x^4)^5
    &=x^{4\cdot 5}\\
    &=x^{20}
    \end{align}

  • \begin{align}
    (a^3)^5
    &=a^{3\cdot 5}\\
    &=a^{15}
    \end{align}

  • \begin{align}
    (a^{-1})^4
    &=a^{(-1)\cdot 4}\\
    &=a^{-4}\\
    &=\frac{1}{x^4}
    \end{align}

Oppgave 4

  • \begin{align}
    (x^{-2})^{-3}
    &=x^{(-2)\cdot (-3)}\\
    &=x^6
    \end{align}

  • \begin{align}
    (b^3)^{-5}
    &=b^{3\cdot(-5)}\\
    &=b^{-15}\\
    &=\frac{1}{b^{15}}
    \end{align}

  • \begin{align}
    ((b^2)^3)^2
    &=b^{2\cdot 3\cdot 2}\\
    &=b^{12}
    \end{align}

  • \begin{align}(y^{14})^{-2}=y^{14\cdot (-2)}=y^{-28}=\frac{1}{y^{28}}\end{align}

Oppgave 5

  • \begin{align}
    (xy^2)^3
    &=x^3\cdot y^{2\cdot 3}\\
    &=x^3y^6
    \end{align}

  • \begin{align}
    (x^2y)^2
    &=x^{2\cdot 2}y^2\\
    &=x^4y^2
    \end{align}

  • \begin{align}
    (a^2b^2c)^2
    &=a^{2\cdot 2}b^{2\cdot 2}c^2\\
    &=a^4b^4c^2
    \end{align}

  • \begin{align}
    (a^3b^2)^{-1}
    &=a^{3\cdot (-1)}b^{2\cdot(-1) }\\
    &=a^{-3}b^{-2}\\
    &=\frac{1}{a^3b^2}
    \end{align}

Oppgave 6

  • \begin{align}
    (a^{-1})^{-3}
    &=a^{(-1)\cdot (-3)}\\
    &=a^3
    \end{align}

  • \begin{align}
    (ab)^7
    &=a^7b^7
    \end{align}

  • \begin{align}
    (a\cdot b\cdot c)^3
    &=a^3b^3c^3
    \end{align}

  • \begin{align}(ab^2c^3)^{-1}=\frac{1}{ab^2c^3}\end{align}