Simplify (xa/by)⁴: Complex Fraction Power Expression

Insert the corresponding expression:

$\left(\frac{x\times a}{b\times y}\right)^4=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:04 According to the laws of exponents, a fraction raised to a power (N)

00:08 equals the numerator and denominator raised to the same power (N)

00:13 We will apply this formula to our exercise

00:20 According to the laws of exponents, when a product is raised to the power (N)

00:23 it is equal to each factor in the product separately raised to the same power (N)

00:28 We will apply this formula to our exercise

00:36 This is the solution

Step-by-Step Solution

To solve this problem, we'll utilize the rules of exponents, particularly the rule for raising fractions to a power.

Step 1: Recognize that the expression $\left(\frac{x \times a}{b \times y}\right)^4$ has a fraction raised to a power.
Step 2: Apply the rule $\left(\frac{m}{n}\right)^p = \frac{m^p}{n^p}$ to distribute the exponent of 4 to both the numerator and the denominator.
Step 3: This means $\left(\frac{x \times a}{b \times y}\right)^4 = \frac{(x \times a)^4}{(b \times y)^4}$ .
Step 4: Use the power of a product rule: $(m \times n)^p = m^p \times n^p$ , which allows us to write $(x \times a)^4$ as $x^4 \times a^4$ and $(b \times y)^4$ as $b^4 \times y^4$ .
Step 5: Substitute these results back into the expression to get $\frac{x^4 \times a^4}{b^4 \times y^4}$ .

Therefore, the simplified expression is $\frac{x^4 \times a^4}{\left(b \times y\right)^4}$ .