Answer: the simplified expression is 5^5x^5y^18
Step-by-step explanation:
To solve this expression using fractional exponents, we can rewrite it as:
3y^2x^5 = (3^1)(y^2)(x^5) = 3^1 * y^2 * x^5
Using the law of raising powers, we can combine the exponents:
3^1 * y^2 * x^5 = 3 * y^2 * x^5
So, the simplified expression is 3yx^5.
2. (5xy^3)^2 • (2xy^4)^3
To solve this expression using fractional exponents, we can rewrite it as:
(5xy^3)^2 • (2xy^4)^3 = (5^1 * x^1 * y^3)^2 • (2^1 * x^1 * y^4)^3 = (5^2 * x^2 * y^6) • (2^3 * x^3 * y^12)
Using the law of raising powers, we can multiply the exponents:
(5^2 * x^2 * y^6) • (2^3 * x^3 * y^12) = 5^(2+3) * x^(2+3) * y^(6+12) = 5^5 * x^5 * y^18
So, the simplified expression is 5^5x^5y^18.