Jawablah Pertanyaan yang Ada pada foto tersebut dengan benar dan teliti ! (Langsung Jawab).... Question from @AASaputra

September 2018 1 81 Report

Jawablah Pertanyaan yang Ada pada foto tersebut dengan benar dan teliti ! (Langsung Jawab)

Takamori37 Mengenal:
$\boxed{a^{-n}=\frac{1}{a^n}}$
Maka,
Nomor 1.
$$\begin{align}\frac{y^{-2}}{5}&=\frac{1}{5}\times\frac{1}{y^2} \\ &=\frac{1}{5y^2}\end{align}$

$$\begin{align}2^{-6}x&=\frac{1}{2^6}\times x \\ &=\frac{x}{2^6}\end{align}$

$$\begin{align}\frac{1}{a^{-5}}&=\frac{1}{^1/_{a^5}} \\ &=a^5\end{align}$

Nomor 2.
Mengingat:
$\boxed{a^p\times a^q=a^{p+q}} \\ \boxed{a^p:a^q=a^{p-q}}$
Maka,
$$\begin{align}3^{-5}\times3^3:3^{-4}&=3^{-5+3-(-4)} \\ &=3^{-2+4} \\ &=3^2\end{align}$

$$\begin{align}(2\times 7)^3\times7^2\times\frac{1}{2\times 7^5}&=2^3\times 7^3\times7^2:(2\times7^5) \\ &=2^{3-1}\times7^{3+2-5} \\ &=2^2\times 7^0 \\ &=4\times 1 \\ &=4\end{align}$

$$\begin{align}\frac{3^0}{9}&=\frac{3^0}{3^2} \\ &=3^{0-2} \\ &=3^{-2} \end{align}$

Nomor 3.
$$\begin{align}2x^4&=2\times\frac{1}{x^{-4}} \\ &=\frac{2}{x^{-4}}\end{align}$

$$\begin{align}\frac{1}{3x^5}&=\frac{1}{3\times\frac{1}{x^{-5}}} \\ &=\frac{x^{-5}}{3}\end{align}$

Nomor 4.
$$\begin{align}\frac{1}{3a^4}:3a^{-2}&=\frac{1}{3a^4}\times\frac{1}{3a^{-2}} \\ &=\frac{1}{9a^{4+(-2)}} \\ &=\frac{1}{9a^2}\end{align}$

$$\begin{align}(a^4\times a^5)^2:a^{-2}&=a^{9\times2}:a^{-2} \\ &=a^{18}:a^{-2} \\ &=a^{18-(-2)} \\ &=a^{20}\end{align}$

$$\begin{align}\frac{(xy)^2}{xy}&=(xy)^{2-1} \\ &=(xy)^1 \\ &=xy\end{align}$

Nomor 5.
$$\begin{align}\frac{a^{-5}b^3}{a^{-1}b^4}\times\frac{a^2b^4}{a^{-3}b^{-1}}&=\frac{a^{-5+2}b^{3+4}}{a^{-1+(-3)}b^{4+(-1)}} \\ &=\frac{a^{-3}b^7}{a^{-4}b^3} \\ &=a^{-3-(-4)}b^{7-3} \\ &=a^{1}b^4 \\ &=ab^4\end{align}$

Nomor 6.
$$\begin{align}\frac{(2^2)^5\times(\frac{1}{2})^4}{(\frac{1}{2})^2\times(2^2)^2}&=\frac{2^{10}\times2^{-4}}{2^{-2}\times 2^4} \\ &=\frac{2^{10+(-4)}}{2^{-2+4}} \\ &=\frac{2^6}{2^2} \\ &=2^{6-2} \\ &=2^4 \end{align}$

Nomor 7.
$$\begin{align}0,36&=\frac{36}{100} \\ &=\frac{9}{25} \\ &=\frac{3^2}{5^2} \\ &=\frac{5^{-2}}{3^{-2}} \\ &=\left[\frac{5}{3}\right]^{-2}\end{align}$

Nomor 8.
$$\begin{align}\frac{x^{3}y^6}{x^{4}y^{-3}}:\frac{x^7y}{xy^{-4}}&=\frac{x^{3-7}y^{6-1}}{x^{4-1}y^{-3-(-4)}} \\ &=\frac{x^{-4}y^5}{x^3y} \\ &=x^{-4-3}y^{5-1} \\ &=x^{-7}y^4 \\ &=\frac{y^4}{x^7}\end{align}$

Nomor 9.
$$\begin{align}25&=5^2 \\ &=\frac{1}{5^{-2}}\end{align}$

Nomor 10.
$$\begin{align}\frac{(xy^3)^{-1}}{(x^{-1}y^2)^3}&=\frac{x^{-1}y^{-3}}{x^{-3}y^6} \\ &=x^{-1-(-3)}y^{-3-6} \\ &=x^2y^{-9} \\ &=\frac{x^2}{y^9}\end{align}$

Nomor 11.
$$\begin{align}\frac{4x^{-4}}{\frac{1}{2}x^{-5}}&=4:\frac{1}{2}\times x^{-4-(-5)} \\ &=4\times 2\times x^{-4+5} \\ &=8x^1 \\ &=8x\end{align}$

Nomor 12.
$$\begin{align}\frac{2^{-2}-3^{-2}}{2^{-1}-3^{-1}}&=\frac{\frac{1}{2^2}-\frac{1}{3^2}}{\frac{1}{2}-\frac{1}{3}} \\ &=\frac{\frac{1}{4}-\frac{1}{9}}{\frac{3-2}{6}} \\ &=\frac{\frac{9-4}{36}}{\frac{1}{6}} \\ &=\frac{5}{36}:\frac{1}{6} \\ &=\frac{5}{6}\end{align}$

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