Simplify 5^-2: Negative Exponent Calculation Step-by-Step

Question

5−2 5^{-2}

Video Solution

Solution Steps

00:00 Solve the following problem
00:03 A negative exponent switches between the numerator and the denominator
00:06 An exponent is the number of times a number is multiplied by itself.
00:09 This is the solution

Step-by-Step Solution

We use the property of powers of a negative exponent:

a−n=1an a^{-n}=\frac{1}{a^n} We apply it to the problem:

5−2=152=125 5^{-2}=\frac{1}{5^2}=\frac{1}{25}

Therefore, the correct answer is option d.

Answer

125 \frac{1}{25}

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

Question Types

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