which expression is equivalent to x^9 y^3/x^3?
A. x^3 y^1
B. x^6 y^0
C. x^6 y^3
D. x^12 y^ 3
The expression x^9 y^3/x^3 can be simplified by subtracting the exponents when dividing exponential terms with the same base.
x^9 y^3/x^3 = x^(9-3) y^(3-0) = x^6 y^3
Therefore, the expression is equivalent to x^6 y^3.
The answer is C. x^6 y^3.
To simplify the expression (x^9 * y^3) / (x^3), we can use the property of dividing like bases by subtracting their exponents.
In this case, we have x raised to the power of 9 divided by x raised to the power of 3. By subtracting the exponents, we get x^(9-3), which simplifies to x^6.
Similarly, we have y raised to the power of 3 divided by y raised to the power of 0. Any non-zero number raised to the power of 0 is always equal to 1. Therefore, y^0 simplifies to 1.
Combining these results, the expression becomes x^6 * 1, which is simply x^6.
So, the answer is option B, x^6 y^0.
To determine which expression is equivalent to x^9 y^3 / x^3, we can simplify the given expression by subtracting the exponents of x.
When we divide two terms with the same base, we subtract the exponents:
x^9 / x^3 = x^(9-3) = x^6
So, the simplified expression is x^6.
Now, we need to divide y^3 by y^0. Any number raised to the power of zero is always 1, so y^0 = 1. Therefore, y^3 / y^0 = y^3.
Combining the simplified x term (x^6) with the simplified y term (y^3), we get the expression x^6 y^3.
Therefore, the answer is C. x^6 y^3, because it is equivalent to x^9 y^3 / x^3.