I am so confused with the rules of exponents. I know them, but I have a hard time applying them because of all the steps. I was wondering if someone would be willing to answer these questions, because I am unsure if my answers are right.
x to the third power y to the negative two power/x to the negative two power times y to the fourth power=
2x to the neg. second power (3x to the fourth - 6x to the econd)=
(-2x to the third)(-3x to the neg second) both expressions to the neg second
(2x to the second y to the negative second) to the third power
(2x to the negative fifth y to the fourth) to the third
Thank you your help is genuinely appreciated.
20v2w4x5 and 12w3x8
Please help me with this
20v2w4x5 and 12w3x8
I'd be happy to help you with your questions on the rules of exponents! Let's go through each problem step-by-step and explain how to solve them.
1. x^3 * y^-2 / x^-2 * y^4:
To simplify this expression, we can divide the same base variables by subtracting their exponents. So, for x terms, we have x^3 / x^-2, which is equivalent to x^(3 - (-2)) or x^5. For y terms, we have y^-2 * y^4, which is equivalent to y^(-2 + 4) or y^2. So the final answer is x^5 * y^2.
2. 2x^-2 * (3x^4 - 6x^2):
To simplify this expression, we need to perform the multiplication and apply the exponent rules. Starting with 2x^-2, we can rewrite this as 2 / (x^2) due to the negative exponent. Now, let's distribute and simplify the expression: (2 / (x^2)) * (3x^4 - 6x^2) = 6x^4 / (x^2) - 12x^2 / (x^2). Simplifying further, we get 6x^(4 - 2) - 12x^(2 - 2) = 6x^2 - 12.
3. (-2x^3)(-3x^-2)^-2:
To solve this expression, let's start by simplifying the term within the parentheses, (-3x^-2)^-2. Applying the exponent, we have (-3)^-2 * (x^-2)^-2. Simplifying the exponent expressions, we get 9 * x^4. Now, we can multiply this with the outside term, -2x^3: (-2x^3)(9x^4) = -18x^(3 + 4) = -18x^7.
4. (2x^2y^-2)^3:
To simplify this expression, we raise each term inside the parentheses to the third power, giving us (2^3) * (x^2)^3 * (y^-2)^3. Simplifying each term, we have 8 * x^(2 * 3) * y^(-2 * 3). This simplifies to 8x^6 * y^(-6). Remember that y^(-6) is equivalent to 1 / y^6, so the final answer is 8x^6 / y^6.
5. (2x^-5y^4)^3:
Similar to the previous problem, we raise each term inside the parentheses to the third power: (2^3) * (x^-5)^3 * (y^4)^3. Simplifying each term further, we have 8 * x^(-5 * 3) * y^(4 * 3). This simplifies to 8x^(-15) * y^12. Remember that x^(-15) is equivalent to 1 / x^15, so the final answer is 8y^12 / x^15.
I hope these explanations help clarify the steps involved in solving exponential expressions. If you have any further questions, feel free to ask!