Question

Evaluate the expression for the given value of the variable. $$(7 t)^{3} \text { when } t=-\frac{3}{7}$$

Short answer

The value of the expression \((7 t)^3\) when \( t = -\frac{3}{7} \) is -1.

Step-by-step solution

Substitute the given value into the expression

First, replace the letter \( t \) in the expression \((7 t)^3\) with the value given for this variable, which is \(-\frac{3}{7}\). We do this by replacing every occurrence of \( t \) in the equation with \(-\frac{3}{7}\). This leads to the following equation: \((7(-\frac{3}{7}))^3\)

Simplify inside the parentheses before the exponent

Next, use multiplication to combine the 7 and -3/7. This simplification gives us: \((-1)^3\)

Raise the result to the power

Now, raise the result in parentheses to the third power. Because the base is -1, \((-1)^3\) simplifies to -1.