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Polynomials, exponents, and scientific notation

Using the power rules with integral exponents
(2s^-1t^3)/(6s^2t-4)^3

9.3*10-5

Computations with scientific notations
9*10^-4/3*10^-6

Evaluating Polynomials
-2x^4 - 3x^2 + 5x -9 for x =2

Multiplying Monomials
-12sq * 3a

Multiplying Polynomials
(3c^2d - d^3 + 1) 8cd^2

Perform the operation
(5x-6)(5x-6)

Use the foil method to find each product
(11x + 3y) (x+4y)

foil method
(5y^3w^2 + 2) (2y^3 w^2 + 3z)

Multiplying Binomials Quickly
(3h -5) (3h + 5)

Product of a sum and difference
( 3y^2 + 1) ( 3y^2 - 1)

Find each product
(3z^4 -8)^2

(2/3y - 1/2)^2

Dividing Monomials
b^19/b^12

-12z^10y^2/-2z^4y^2

Dividing a polynomial by a monomial
5y^3 -10/-5

Write the expression in the form
quotient + remainder/divisor

2x^2 + 4/ 2x

Area of a dot. If the radius of a very small circle is 2.35 * 10^-8 centimeters, then what is the circle's area?

Perimeter of a rectangle. The perimeter of a rectangular backyard is 6x + 6 yards. If the width is x yards, find a binomial that represents the length.

Solution Preview

Please open attachment for solution.

Using the power rules with intergral exponents
(2s^-1t^3)/(6s^2t-4)^3

(2s-1 t3)/(6s2t-4)3 = (2t3t12)/(216s6s) = (2t15)/(216s7) = (t15)/(108s7)

9.3*10-5
= 0.000093

Computations with scientific notations
9*10^-4/3*10^-6
= 9 (10-4/3) * 10-6
= 9 / ((104/3) * 106)
= 9 / (1022/3)

Evaluating Polynomials
-2x^4 - 3x^2 + 5x -9 for x =2
= -2 (2)4 - 3(2)2 + 5(2) - 9
= -32 - 12 + 10 - 9
= ...

Solution Summary

This provides examples of working with exponents, scientific notations, and polynomials, including operations and evaluation. It also includes area and perimeter word problems.

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