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a) \(\left(2\frac{1}{3}x^2y^3z\right)^{10}.\left(\frac{-3}{7}x^5y^4z^2\right)^{10}.axyz\)
=\(\left(2\frac{1}{3}x^2y^3z.\frac{-3}{7}x^5y^4z^2\right)^{10}.axyz\)
=\(\left(\frac{7}{3}.\frac{-3}{7}x^2.x^5.y^3.y^4.z.z^2\right)^{10}.axyz\)
=\(\left(-1.x^7y^7z^3\right)^{10}.axyz\)
=\(x^{70}.y^{70}z^{30}.axyz\)
=\(a.x^{71}.y^{71}.z^{31}\)
PHS: a
PB: x71.y71.z31
Bậc: 173
a) \(A=\left(\dfrac{1}{2^3}.3.\dfrac{13}{3}\right)\left(a^{3+2+1}\right)\left(x^{1+3}\right)\left(y^{1+2}\right)=\dfrac{13}{8}.a^6.x^4.y^3\)
\(B=\left[2^k.\left(-\dfrac{1}{2}\right)^2\right]\left(x^{2k+2}\right)\left(y^{3k+2.2}\right)\left(z^{4k+}\right)=2^{k-2}.x^{2\left(k+1\right)}.y^{3k+4}.z^{4k}\)
thu gọn : -a.(x. x^2).(y.y^6).(-b)= -a.x^3.y^7.(-b)
hệ số là :-a và -b
phần biến là :x và y
bậc :10
a)\(-\left(\frac{-1}{2}xy^2z\right)^2\left(4x^2yz^3\right)\)
\(=-\left(\frac{1}{4}x^2y^4z^2\right)\left(4x^2yz^3\right)\)
\(=\left(\frac{-1}{4}.4\right)\left(x^2x^2\right)\left(y^4y\right)\left(z^2z^3\right)\)
\(=-x^4y^5z^5\) \(\Rightarrow\)Bậc là 14 Hệ số là -1
b)\(\left(\frac{-1}{3}x^2yz^3\right).\left(\frac{-6}{7}xyz^2\right)\)
\(=\left(\frac{-1}{3}.\frac{-6}{7}\right)\left(x^2x\right)\left(yy\right)\left(z^3z^2\right)\)
\(=\frac{2}{7}x^3y^2z^5\) \(\Rightarrow\)Bậc là 10 Hệ số là \(\frac{2}{7}\)
c)\(-3x^2.y^4.\left(\frac{-1}{3}y^4z^5x\right).\left(\frac{-1}{2}zyx^3\right)\)
\(=\left(-3.\frac{-1}{3}.\frac{-1}{3}\right)\left(x^2xx^3\right)\left(y^4y^4y\right)\left(z^5z\right)\)
\(=\frac{-1}{3}x^6y^9z^6\) \(\Rightarrow\)Bậc là 21 Hệ số là \(\frac{-1}{3}\)
d)\(\frac{3}{4}xy^3\left(\frac{-2}{3}x^2y^4\right)^2\)
\(=\frac{3}{4}xy^3\left(\frac{4}{9}x^4y^{16}\right)\)
\(=\left(\frac{3}{4}\cdot\frac{4}{9}\right)\left(xx^4\right)\left(y^3y^{16}\right)\)
\(=\frac{1}{3}x^5y^{19}\)
a) \(2x^2y^3.\dfrac{1}{4}xy^3\left(-3\right)xy\)
\(=\left(-3.2.\dfrac{1}{4}\right)x^4y^7\)
\(=\dfrac{-3}{2}x^4y^7\)
\(\Rightarrow Hệ\) số: \(\dfrac{-3}{2}\)
Phần biến: \(x^4y^7\)
b) \(\left(-2x^3y\right)^2.xy^2.\dfrac{1}{5}y^5\)
\(=\dfrac{4}{5}x^7y^9\)
\(\Rightarrow Phần\) biến: \(x^7y^9\)
Hệ số: \(\dfrac{4}{5}.\)
a/ \(2x^2y^3\cdot\dfrac{1}{4}xy^3\left(-3xy\right)\)
\(=\left[2\cdot\dfrac{1}{4}\cdot\left(-3\right)\right]\left(x^2.x.x\right)\left(y^3.y^3.y\right)\)
\(=-\dfrac{3}{2}x^4y^7\)
Phần biến: \(x^4y^7\)
Hệ số: \(-\dfrac{3}{2}\)
b/ \(\left(-2x^3y\right)^2\cdot xy^2\cdot\dfrac{1}{5}y^5=4x^6y^2\cdot xy^2\cdot\dfrac{1}{5}y^5\) \(=4\cdot\dfrac{1}{5}\left(x^6\cdot x\right)\left(y^2\cdot y^2\cdot y^5\right)=\dfrac{4}{5}x^7y^9\)
Phần biến: \(\dfrac{4}{5}\)
Hệ số: \(x^7y^9\)
1.a)\(2.x-\dfrac{5}{4}=\dfrac{20}{15}\)
\(\Leftrightarrow2.x=\dfrac{20}{15}+\dfrac{5}{4}=\dfrac{4}{3}+\dfrac{5}{4}=\dfrac{16+15}{12}=\dfrac{31}{12}\)
\(\Leftrightarrow x=\dfrac{31}{12}:2=\dfrac{31}{12}.\dfrac{1}{2}=\dfrac{31}{24}\)
b)\(\left(x+\dfrac{1}{3}\right)^3=\left(-\dfrac{1}{8}\right)\)
\(\Leftrightarrow\left(x+\dfrac{1}{3}\right)^3=\left(-\dfrac{1}{2}\right)^3\)
\(\Leftrightarrow x+\dfrac{1}{3}=-\dfrac{1}{2}\)
\(\Leftrightarrow x=-\dfrac{1}{2}-\dfrac{1}{3}=-\dfrac{5}{6}\)
2.Theo đề bài, ta có: \(\dfrac{a}{2}=\dfrac{b}{3}\) và \(a+b=-15\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{a+b}{2+3}=\dfrac{-15}{5}=-3\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{a}{2}=-3\Rightarrow a=-6\\\dfrac{b}{3}=-3\Rightarrow b=-9\end{matrix}\right.\)
3.Ta xét từng trường hợp:
-TH1:\(\left\{{}\begin{matrix}x+1>0\\x-2< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x>-1\\x< 2\end{matrix}\right.\)\(\Rightarrow x\in\left\{0;1\right\}\)
-TH2:\(\left\{{}\begin{matrix}x+1< 0\\x-2>0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x< -1\\x>2\end{matrix}\right.\)\(\Rightarrow x\in\varnothing\)
Vậy \(x\in\left\{0;1\right\}\)
4.\(B=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{9}{49}\right)^9=\left(\dfrac{3}{7}\right)^{21}:\left[\left(\dfrac{3}{7}\right)^2\right]^9=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{3}{7}\right)^{18}=\left(\dfrac{3}{7}\right)^3=\dfrac{27}{343}\)
\(=\dfrac{8}{3}\cdot x^2y^3z\cdot\dfrac{7^{10}}{3^{10}}\cdot x^{50}y^{40}\cdot z^{20}\cdot axyz\)
\(=\left(\dfrac{8}{3}\cdot\dfrac{7^{10}}{3^{10}}\cdot a\right)\cdot x^{53}y^{44}z^{22}\)
Hệ số là \(\dfrac{8}{3}\cdot\dfrac{7^{10}}{3^{10}}\cdot a\)
Bậc là 119