Simplify the Expression: (3^8 × a^8)/(x^8 × 5^8)

Insert the corresponding expression:

$\frac{3^8\times a^8}{x^8\times5^8}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, a product that is raised to the power (N)

00:07 is equal to the product broken down into factors where each factor is raised to the power (N)

00:11 We will apply this formula to our exercise, in the reverse direction

00:18 We'll combine the factors into a multiplication operation within parentheses

00:28 According to the laws of exponents, a fraction raised to the power (N)

00:33 equals a fraction where the both numerator and denominator are raised to the power (N)

00:36 We will apply this formula to our exercise, in the reverse direction

00:42 We'll place the entire fraction inside of parentheses and raise it to the appropriate power

00:45 This is the solution

Step-by-Step Solution

To solve this problem, we'll rewrite the given fraction $\frac{3^8 \times a^8}{x^8 \times 5^8}$ using the rules of powers and exponents.

Step 1: Recognize the overall structure of the fraction is $\frac{m^8 \times n^8}{p^8 \times q^8}$ .
Step 2: Apply the rule of exponents to express it as a single power of the entire fraction: $\left(\frac{m \times n}{p \times q}\right)^8$ .
Step 3: Substitute the values: $\left(\frac{3 \times a}{x \times 5}\right)^8$ simplifies the expression effectively, given that all components are non-zero.

Thus, by applying the exponent rule directly to the entire fraction, we simplify to $\left(\frac{3 \times a}{x \times 5}\right)^8$ .