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vlada-n [284]
1 year ago
8

P³ = 1/8 please help me if anybody can .

Mathematics
2 answers:
Leya [2.2K]1 year ago
6 0
P would be equal to 1/2
ivanzaharov [21]1 year ago
3 0

Answer:

p= \dfrac{1}{2}

Step-by-step explanation:

Given equation:

p^3=\dfrac{1}{8}

Cube root both sides:

\implies \sqrt[3]{p^3}= \sqrt[3]{\dfrac{1}{8}}

\implies p= \sqrt[3]{\dfrac{1}{8}}

\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:

\implies p= \left(\dfrac{1}{8}\right)^{\frac{1}{3}}

\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:

\implies p= \dfrac{1^{\frac{1}{3}}}{8^{\frac{1}{3}}}

\textsf{Apply exponent rule} \quad 1^a=1:

\implies p= \dfrac{1}{8^{\frac{1}{3}}}

Rewrite 8 as 2³:

\implies p= \dfrac{1}{(2^3)^{\frac{1}{3}}}

\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:

\implies p= \dfrac{1}{2^{(3 \cdot \frac{1}{3})}}

Simplify:

\implies p= \dfrac{1}{2^{\frac{3}{3}}}

\implies p= \dfrac{1}{2^{1}}

\implies p= \dfrac{1}{2}

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