Simplify each of the following expressions. Be sure that your answer has no negative or fractional exponents.
(2x^2•y^-3)(3x^-1y^5)
(2y^2)/3
think that's right
I do not see a division
6 x^1 y^2
there are negative exponents which move it to the denominator.
x^2 x^-1 = x^1
or
x^2/x^1 = x^1
also
y^5/y^3 = y^2
To simplify the expression (2x^2 • y^-3)(3x^-1y^5), we can follow these steps:
Step 1: Multiply the coefficients (numbers) together. In this case, we have 2 and 3, so their product is 2 x 3 = 6.
Step 2: Multiply the variables with the same base together. In this case, we have x's and y's.
For the x's:
- Multiply the coefficients (exponents) together: 2 x (-1) = -2.
- Write x^-2 as 1/x^2 (since a negative exponent indicates taking the reciprocal).
- Multiply the variables: x^2 • 1/x^2 = 1 (the x terms cancel out).
For the y's:
- Multiply the coefficients (exponents) together: -3 + 5 = 2 (add the exponents since they have the same base y).
- Write y^2 as y^2 (leave it as it is since the exponent is positive).
Step 3: Combine the simplified variables and coefficients together. In this case, we have 1 (from the x terms) multiplied by y^2 (from the y terms). Therefore, we can rewrite the expression as 6y^2.
So, the simplified expression is 6y^2.