5.7: Nguvu ya utawala wa bidhaa kwa watetezi

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Page ID: 164578

Victoria Dominguez, Cristian Martinez, & Sanaa Saykali
Citrus College via ASCCC Open Educational Resources Initiative

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Nguvu ya utawala wa bidhaa kwa watazamaji itashughulika na maneno ambapo bidhaa ya besi hufufuliwa kwa nguvu fulani.

Ufafanuzi: Nguvu ya Utawala wa Bidhaa kwa Watazamaji

Kwa idadi yoyote halisi a na b na idadi yoyote n, nguvu ya utawala wa bidhaa kwa exponents ni yafuatayo:

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

Mfano Template:index

Kurahisisha maneno yafuatayo

\((a \cdot b)^3\)

Suluhisho

\(\begin{aligned} &(a \cdot b) 3&& \text{Given} \\ &a \cdot b \cdot a \cdot b \cdot a \cdot b &&\text{Expand using exponent 3} \\ &a \cdot a \cdot a \cdot b \cdot b \cdot b &&\text{Reorder product using the commutative property.} \\ &a^3b^3 && \text{Simplify to single base.} \end{aligned}\)

Mfano Template:index

Kurahisisha kujieleza kwa kutumia nguvu ya utawala wa bidhaa kwa exponents.

\((2x^3y^2 )^2 \)

Suluhisho

\(\begin{aligned} &((2x^3y^2 )^2 ) &&\text{Given} \\ &= 2^2 \cdot x^{3\cdot 2 } \cdot y^{2\cdot 2 } &&\text{Power of a product rule applied} \\ &= 4x ^6y^4 &&\text{Simplify by multiplying exponents} \end{aligned}\)

Mfano Template:index

Kurahisisha kujieleza kwa kutumia nguvu ya utawala wa bidhaa kwa exponents.

\((2x^5 \cdot 3y)^3\)

Suluhisho

\(\begin{aligned} &(2x^5 \cdot 3y)^3 &&\text{Given}\\ &= (6x^5 y)^3 &&\text{If possible, simplify inside the parentheses.} \\ &= 6^3 \cdot x^{5\cdot 3 } \cdot y^3 &&\text{Power of a product rule for exponents applied.} \\ &216x^{15}y^3 &&\text{Simplify by multiplying as needed.} \end{aligned}\)

Mfano Template:index

Kurahisisha kujieleza kwa kutumia nguvu ya utawala wa bidhaa kwa exponents.

\((3ab^4 )^{−2}\)

Suluhisho

\(\begin{aligned} &(3ab^4 )^{−2 } && \text{Given} \\ &= \dfrac{1 }{(3ab^4)^2 } &&\text{Negative exponent rule applied} \\ &= \dfrac{1 }{3^2 \cdot a^3 \cdot b^{4\cdot 2}}&&\text{Power of a product rule applied.} \\ &\dfrac{1 }{9a^3b^8 } &&\text{Simplify by multiplying as needed.} \end{aligned}\)

Zoezi Template:index

Kurahisisha usemi kwa kutumia nguvu ya utawala wa bidhaa kwa exponents.

\((xy^2 ) ^3\)
\((2xy^2z ^3 ) ^7\)
\((x^ 2 ) ^{−3}\)
\((x ^2y) ^{−3}\)
\((2r ^4 )^ 5\)
\((−2p^ 7 )^ 7\)
\((3k \cdot 2j^2 )^5\)