Rewrite each expression with positive exponents and simplify.
X^2•x^n/x^3•x^n
What does this question mean? Do I just cancel things out? Please help
x^2 * x^n x^(2+n)
x^3 * x^n = x^(3+n)
now, after the division, subtracting powers, you have
x^((2+n)-(3+n)) = x^-1 = 1/x
You can see that this is so, because in the original fraction, you can cancel the x^n factors, leaving just
x^2/x^3 = 1/x
To rewrite the expression with positive exponents, you need to use the laws of exponents. Here's how you can simplify the expression step by step:
1. Start with the given expression:
X^2 * x^n / x^3 * x^n
2. To simplify this expression, you can use the property of multiplication with exponents. According to this property, when you multiply two terms with the same base, you add their exponents.
So, in the numerator (X^2 * x^n), add the exponents together:
(X^2 * x^n) = X^(2 + n)
3. In the denominator (x^3 * x^n), also add the exponents together:
(x^3 * x^n) = x^(3 + n)
4. After simplifying the numerator and denominator, rewrite the expression:
X^(2 + n) / x^(3 + n)
5. Finally, use the property of division with exponents. According to this property, when you divide two terms with the same base, you subtract their exponents.
In this case, subtract the exponent of x in the denominator from the exponent of X in the numerator:
X^(2 + n) / x^(3 + n) = X^(2 + n - (3 + n))
Simplify the exponents:
X^(2 + n - 3 - n) = X^(-1)
6. As a final step, if X is a variable, you can rewrite X^(-1) as 1/X:
X^(-1) = 1/X
Therefore, the simplified expression is 1/X.
Note: Cancelling terms out is not appropriate when dealing with exponents. Instead, you should simplify the exponents using the properties of exponents and then simplify further if possible.