Question

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

Answer 1

p would be equal to 1/2

Answer 2

`p= (1)/(2)`

Explanation:

Given equation:

`p^3=(1)/(8)`

Cube root both sides:

`\implies \sqrt[3]{p^3}= \sqrt[3]{(1)/(8)}`

`\implies p= \sqrt[3]{(1)/(8)}`

`\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{(1)/(n)}:`

`\implies p= \left((1)/(8)\right)^{(1)/(3)}`

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

`\implies p= \frac{1^{(1)/(3)}}{8^{(1)/(3)}}`

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

`\implies p= \frac{1}{8^{(1)/(3)}}`

Rewrite 8 as 2³:

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

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

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

Simplify:

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

`\implies p= (1)/(2^(1))`

`\implies p= (1)/(2)`