Which expression is equivalent to [tex] \frac{X^{-1}Y^{4}}{3x^{-5}y^{-1}} [/tex]?

Whenever you have negative exponents over a variable, what you want to do is move that variable to the other side of the fraction and make the exponent positive. For this expression, the first step would therefore become x^5y^5 / 3x. (Exponents with the same coefficient are added together to get y^5.) Then, when you have like coefficients in the numerator and the denominator, you subtract those exponents. Your final answer is therefore x^4y^5 / 3.

Answered by Sphinx | 2024-06-10

The student is asking for help simplifying a given algebraic expression involving exponents and variables.
The expression is X^-1Y^4 / 3x^-5y^-1, which simplifies using the laws of exponents.
To simplify, we can combine the exponents by subtracting the exponents of like bases and considering the negative exponent represents the reciprocal of that base. Here are the steps to simplify the expression:
Combine the exponents of x:
The negative exponents indicate reciprocals, so x^-1 becomes 1/x and x^-5 becomes 1/x^5. Taking the reciprocal of 1/x^5 and multiplying by 1/x gives us x^5/x = x^(5-1) = x^4.
Combine the exponents of y:
Similarly, y^4 multiplied by the reciprocal of y^-1 gives us y^(4+1) = y^5.
Divide everything by the constant 3.
Thus, the simplified expression is x^4y^5 / 3.

Answered by BillDuke | 2024-06-24

The expression 3 X − 5 Y − 1 X − 1 Y 4 ​ simplifies to 3 X 4 Y 5 ​ by moving negative exponents to the opposite side of the fraction and combining like terms. We combine and simplify the exponents in both the numerator and the denominator to arrive at the final expression. The steps include rewriting negative exponents, combining bases, and subtracting exponents of the same base.
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Answered by Sphinx | 2024-11-03