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PLEASE HELP!

Solve the following expressions using fractional exponents and laws of raising powers.

1. (3y^2x^5)

2. (5xy^3)^2 • (2xy^4)^3

User Markis
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1 Answer

6 votes

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.

User Leifparker
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