Question

evaluate the expression $p^3 - q^4 + 3r \div 2$ for $p = 6$, $q = 2$, and $r = 4$. show your work.

Explanation:

Step1: Substitute the values

Substitute \( p = 6 \), \( q = 2 \), and \( r = 4 \) into the expression \( p^{3}-q^{4}+3r\div2 \).
We get \( 6^{3}-2^{4}+3\times4\div2 \).

Step2: Calculate each term

• Calculate \( 6^{3} \): \( 6^{3}=6\times6\times6 = 216 \).
• Calculate \( 2^{4} \): \( 2^{4}=2\times2\times2\times2 = 16 \).
• Calculate \( 3\times4\div2 \): First, \( 3\times4 = 12 \), then \( 12\div2 = 6 \).

Step3: Combine the terms

Now substitute the calculated values back into the expression:
\( 216-16 + 6 \).
First, \( 216-16=200 \), then \( 200 + 6 = 206 \).

Answer:

\( 206 \)