Simplify the Power Fraction: (20^4)/(31^4) Calculation

Insert the corresponding expression:

$\frac{20^4}{31^4}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:05 According to the exponent laws, a fraction raised to the power (N)

00:11 equals the numerator and denominator, each raised to the same power (N)

00:17 We'll apply this formula to our exercise, only this time in the opposite direction

00:25 This is the solution

Step-by-Step Solution

To solve this problem, we need to rewrite the given expression $\frac{20^4}{31^4}$ using properties of exponents.

Let's take these steps:

Step 1: Recognize the expression as a fraction raised to a power. The problem provides $\frac{20^4}{31^4}$ .
Step 2: Apply the power of a fraction rule: For any real numbers $a$ and $b$ , and a positive integer $n$ , $\left( \frac{a}{b} \right)^n = \frac{a^n}{b^n}$ .

Applying Step 2, we write:

$\frac{20^4}{31^4} = \left(\frac{20}{31}\right)^4$ .

Thus, the corresponding expression is $\left(\frac{20}{31}\right)^4$ .

Therefore, the solution to the problem is $\left(\frac{20}{31}\right)^4$ .