5.2: Utawala wa Bidhaa kwa Watazamaji
- Page ID
- 164589
Kwa idadi yoyote halisi\(a\) na idadi chanya\(m\) na\(n\), utawala wa bidhaa kwa exponents ni yafuatayo.
\(a^m \cdot a^n = a^{m+n}\)
Kumbuka: Msingi lazima iwe sawa kutumia utawala wa bidhaa.
Wazo:
Kutoka sehemu ya mwisho,\(x^3 = \textcolor{blue}{ x \cdot x \cdot x }\qquad x^5 = \textcolor{red}{x \cdot x \cdot x \cdot x \cdot x}\)
Bidhaa zao
\(x^3 \cdot x^5 = \textcolor{blue}{x \cdot x \cdot x} \textcolor{red}{\cdot x \cdot x \cdot x \cdot x \cdot x} = x^8\)
Hivyo,\(x^3 \cdot x^5 = x^{3+5 }= x^8\)
Tumia utawala wa bidhaa wa watazamaji ili kurahisisha maneno.
- \(k^3 \cdot k^9\)
- \(\left(\dfrac{2 }{7}\right)^2 \cdot \left(\dfrac{2 }{7}\right)^6\)
- \((−2a)^3 \cdot (−2a)^7\)
- \(x \cdot x^3 \cdot x^{11}\)
- \(y^{13 }\cdot y^{33}\)
- \(x^3 \cdot y^2 \cdot x \cdot y^4\)
Suluhisho
Ufafanuzi | Utawala wa Bidhaa | Msingi |
\(k^3 \cdot k^9\) | \(k^{3+9}= k^{12}\) | \(k\) |
\(\left(\dfrac{2 }{7}\right)^2 \cdot \left(\dfrac{2 }{7}\right)^6\) | \(\left( \dfrac{2 }{7}\right)^{2+6 }= \left(\dfrac{2 }{7}\right)^8\) | \(\dfrac{2}{7}\) |
\((−2a)^3 \cdot (−2a)^7\) | \((−2a)^{3+7 }= (−2a)^{10}\) | \(-2a\) |
\(x \cdot x^3 \cdot x^{11}\) | \(x ^{1+3+11 }= x^{15}\) | \(x\) |
\(y^{13 }\cdot y^{33}\) | \(y^{13+33 }= y^46\) | \(y\) |
\(x^3 \cdot y^2 \cdot x \cdot y^4\) | \(x^{3+1 }\cdot y ^{2+4 }= x^{ 4 }\cdot y^{6}\) | \(x\)na\(y\) |
Kumbuka: Tena, besi lazima iwe sawa ili kurahisisha kutumia utawala wa bidhaa wa exponent
Hatua muhimu ili kurahisisha kutumia utawala wa bidhaa wa exponents:
- Tambua maneno na misingi ya kawaida
- Kutambua exponent ya besi ya kawaida.
- Kuongeza exponents ya besi ya kawaida na kufanya matokeo ya jumla exponent mpya.
- Kurudia hatua kama unahitaji
Tumia utawala wa bidhaa wa wafuatiliaji ili kurahisisha zifuatazo.
- \(f^3 \cdot f^11\)
- \(\left(\dfrac{x}{7}\right)^2 \cdot \left(\dfrac{x }{7}\right)^3\)
- \((−7x)^9 \cdot (−7x)^7\)
- \(h^5 \cdot h^3 \cdot h^{11}\)
- \(t^{13} \cdot t^{33}\)
- \(x^8 \cdot y^2 \cdot z \cdot x^ 3 \cdot y^2 \cdot z^{17}\)
- \(x^3 \cdot y^4 \cdot x^3\)