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

Question

Insert the corresponding expression:

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

00:00 Simply

00:03 According to exponent laws, a product entirely in power (N)

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

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

00:20 According to exponent laws, a power on the entire fraction of degree (N)

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

00:29 Now we'll use the second formula and convert to a fraction in parentheses with exponent

00:34 And this is the solution to the question

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