Chapter 4, Problem 8CST

To determine

To determine which expression is equivalent to $3^{-4}{x}^0$

Answer to Problem 8CST

F. $\frac{1}{81}$

Explanation of Solution

Given information:

Expression $3^{-4}{x}^0$

Formula Used: Negative Exponent Rule and Zero Exponent Rule

Calculation:

As the exponent of 3 here is negative, apply the negative exponent rule which says that when exponent is negative, the numerator & denominators are reversed to change the exponent to positive.

  $3^{-4}=\frac{1}{3^4}$

Since the exponent of x is zero, apply the zero exponent rule here which says any number with the exponent 0 is evaluated as 1. This gives us-

  $3^{-4}{x}^0=\frac{1}{3^4}\times 1$

And finally,

  $=\frac{1}{3\times 3\times 3\times 3}=\frac{1}{81}$

Hence F is correct.

Conclusion-

F. $\frac{1}{81}$