Simplify the Exponential Fraction: (5¹⁰ × 8¹⁰)/(4¹⁰ × 7¹⁰)

Question

Insert the corresponding expression:

$\frac{5^{10}\times8^{10}}{4^{10}\times7^{10}}=$

00:00 Simplify the following problem

00:03 According to the exponent laws, a product raised to the power (N)

00:07 equals the product broken down into factors with each factor raised to the power (N)

00:11 We'll apply this formula to our exercise, converting to parentheses with an exponent

00:20 According to the exponent laws, a fraction raised to a power (N)

00:24 equals the numerator and denominator, each raised to the same power (N)

00:29 Now we'll apply the second formula and convert the expression to a fraction within parentheses with an exponent

00:34 This is the solution

$\frac{\left(5\times8\right)^{10}}{\left(4\times7\right)^{10}}$