How Would You Solve These?

Question

I really don't get these problems.

Here are a few examples and I can do the rest myself.

Simplify the following expressions completely.

46. (2xy)(3x to the third power y)

48. (t to the third power)to the second power

50. 4x to the negative third power

51. (2x)to the negative first power

52. 3x to the third power times y to the third power over two and then the whole thing to the fourth power

53. 7x to the third power minus 3x to the third power

56. (4xy to the third power) over (2y squared)to the third power

57. (12x to the third power y) to the second power times (-1x to the third power y to the fourth power) to the third power.

and if you need to solve sine, cosine, and tangent of an angle, do you need to know the angle measure?

and if you have to draw a reflection of a shape, and part of it is on the line, how do you do that?

Please and Thank You=]

Answer 1

these should get you started.  Basic principle is when you raise a power to a power, you multiply the exponents. And, when you multiply variables with exponents, you add the exponents.  Neg exponents basically means you move the number to the other side of the line (see #50)

46. (2xy)(3x^3y) = 6x^4y^2

48. (t^3)^2 = t^6

50. 4x ^-3 = 4/x^3

51. (2x)^-1 = 1/2x

52. (3x^3y^3/two)^4 = 81x^12y^12/16

53. 7x^3- 3x^3 = 4x^3

56. (4xy^3)/(2y^2)^3 = 4xy^3/8y^6 = x/2y^3 = xy^-3/2

57. (12x^3y)^2 (-1x^3y^4)^3 = 144x^3y^2(-1x^9y^12) = -144x^12y^14