If `2=p^(3)`, then 8p must equal

Options

A. `p^(6)`
B. `p^(8)`
C. `p^(10)`
D. `8sqrt(2)`

Answer

To solve the equation \(2 = p^3\) and find the value of \(8p\), we can follow these steps:

### Step 1: Express \(8\) in terms of \(2\)
We know that:
\[ 8 = 2^3 \]

### Step 2: Substitute \(2\) with \(p^3\)
Since we have \(2 = p^3\), we can substitute \(2\) in the expression for \(8\):
\[ 8 = (p^3)^3 \]

### Step 3: Simplify the expression
Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we can simplify:
\[ 8 = p^{3 \cdot 3} = p^9 \]

### Step 4: Now calculate \(8p\)
We need to find \(8p\):
\[ 8p = p^9 \cdot p \]

### Step 5: Combine the exponents
Using the property \(a^m \cdot a^n = a^{m+n}\), we can combine the exponents:
\[ 8p = p^{9+1} = p^{10} \]

### Final Answer
Thus, \(8p\) must equal \(p^{10}\).

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