Calculate 7^(-4): Evaluating Negative Integer Exponents

Question

$7^{-4}=\text{?}$

00:00 Solve

00:03 According to power laws, any number(A) to the power of(-N)

00:06 equals 1 divided by the number(A) to the power of(N)

00:09 Let's apply to the question, the formula works from number to fraction and vice versa

00:12 We got 1 divided by (7) to the power of (4)

00:15 Let's solve 7 to the power of 4 using power laws

00:22 And this is the solution to the question

We must first remind ourselves of the negative exponent rule:

$a^{-n}=\frac{1}{a^n}$ When applied to given the expression we obtain the following:

$7^{-4}=\frac{1}{7^4}=\frac{1}{2401}$

Therefore, the correct answer is option C.

$\frac{1}{2401}$