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

Insert the corresponding expression:

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

Video Solution

Solution Steps

00:08 Let's simplify this problem together.

00:13 Remember, with exponent laws, if a fraction is raised to the power of N

00:19 it means both the numerator and the denominator are raised to that same power N.

00:26 We'll use this idea now, but in reverse, to solve the problem.

00:33 And here is our solution. Great job!

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