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

Question

$5^{-2}$

00:00 Simply

00:09 Any number to the power of 1 is always equal to itself

00:20 We'll use the formula for negative powers

00:23 When we have a negative power (-M) on any fraction (A/B)

00:27 We get the reciprocal number (B/A) raised to the positive exponent (M)

00:35 We'll use this formula in our exercise

00:39 We'll substitute the reciprocal number and the opposite power

00:44 Now we'll use the formula for powers of fractions

00:50 We'll make sure to raise both numerator and denominator to the appropriate power

00:55 We'll use this formula in our exercise

00:58 We'll make sure to raise both numerator and denominator to the power, and calculate

01:03 And this is the solution to the question

We use the property of powers of a negative exponent:

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

$5^{-2}=\frac{1}{5^2}=\frac{1}{25}$

Therefore, the correct answer is option d.

$\frac{1}{25}$