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

Question

7−4=? 7^{-4}=\text{?}

Video Solution

Solution Steps

00:00 Solve the following problem
00:03 According to the power laws, a number(A) when raised to the power of(-N)
00:06 equals 1 divided by the number(A) raised to the power of(N)
00:09 Let's apply this to the question, the formula works from number to fraction and vice versa
00:12 We obtain 1 divided by (7) raised to the power of (4)
00:15 Let's proceed to solve 7 raised to the power of 4 using the power laws
00:22 This is the solution

Step-by-Step Solution

We must first remind ourselves of the negative exponent rule:

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

7−4=174=12401 7^{-4}=\frac{1}{7^4}=\frac{1}{2401}

Therefore, the correct answer is option C.

Answer

12401 \frac{1}{2401}

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Related Subjects

Negative Exponents Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Exponents - Special Cases

Question Types

Negative Exponents: Presenting powers with negative exponents as fractions Negative Exponents: Calculating powers with negative exponents Applying Combined Exponents Rules: Presenting powers with negative exponents as fractions Applying Combined Exponents Rules: Calculating powers with negative exponents Applying Combined Exponents Rules: Monomial