Convert the Expression: Writing 1/5² in Standard Form

Question

Insert the corresponding expression:

$\frac{1}{5^2}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, a number raised to the power of (-N)

00:06 is equal to its reciprocal raised to the opposite power (N)

00:09 We will apply this formula to our exercise

00:12 We'll convert to the reciprocal number and raise it to the opposite power (times(-1))

00:15 This is the solution

Step-by-Step Solution

To solve the given problem, we need to express $\frac{1}{5^2}$ using negative exponents. We'll apply the formula for negative exponents, which is $\frac{1}{a^n} = a^{-n}$ :

Identify the base and power in the denominator. Here, the base is $5$ and the power is $2$ .
Apply the inverse formula: $\frac{1}{5^2} = 5^{-2}$ .

Thus, the equivalent expression for $\frac{1}{5^2}$ using a negative exponent is $5^{-2}$ .

Answer

$5^{-2}$

Related Subjects

Question Types

Powers of a Fraction: Inverse formula Powers of a Fraction: Presenting powers in the denominator as powers with negative exponents Negative Exponents: Presenting powers in the denominator as powers with negative exponents