Question

In the following exercises, evaluate the following expressions.

When $x=4$

localid="1644427040415" $$\begin{gathered} \left(\text{a}\right)x^3 \\ \left(\text{b}\right)5^x \\ \left(\text{c}\right)2x^2-5x+3 \end{gathered}$$

Short answer

The values of the given expressions are

$\left(\text{a}\right)64$

$\left(\text{b}\right)625$

$\left(\text{c}\right)13$

Step-by-step solution

Step 1. Given information

The value of $x=4$

$$\begin{gathered} \left(\text{a}\right)x^3 \\ \left(\text{b}\right)5^x \\ \left(\text{c}\right)2x^2-5x+3 \end{gathered}$$

Part a.Step 1. Evaluate the expression

$\left(\text{a}\right)$

localid="1644047873541" width="193" style="max-width: none; vertical-align: -36px; user-select: auto;" $$\begin{gathered} x^3=4^3(\text{use}x=4) \\ =4\times 4\times 4 \\ =64 \end{gathered}$$

Hence, the value of the expression is 64.

Part b.Step 1. Evaluate the expression

$\left(\text{b}\right)$

$$\begin{gathered} 5^x=5^4 \\ =5\times 5\times 5\times 5 \\ =625 \end{gathered}$$

Hence, the value of the expression is 625.

Part c.Step 1.Evaluate the expression

$\left(\text{c}\right)$

$$\begin{gathered} 2x^2-5x+3=2{\left(4\right)}^2-5\left(4\right)+3 \\ =2\left(16\right)-20+3 \\ =30-17 \\ =13 \end{gathered}$$

Hence, the value of the expression is 13.