Question

simplify using properties of exponents. answers should have positive exponents. for example ( 5^3 = 125 ). each set of problems will use the property listed above or properties attempted in previous sets.

zero exponent properties

1. ( (c^{18})^{-1} = )
2. ( (3d^2)^0 = )
3. ( 5(x^0)y^{-1} = )

1. ( (2d^7)(-4d^9d^5) = )
2. ( (9x^{10}y^3)(-x^5y^3) = )

1. ( \frac{2d^7}{-4d^9d^5} = )
2. ( \frac{9x^{10}y^3}{-x^5y^3} = )

1. ( (d^5)^{-2} = )
2. ( (6x^3y)(x^2)^{-2} = )

Explanation:

Step1: Solve problem 8

Multiply coefficients, add exponents of like bases.
$$(9x^{10}y^3)(-x^5y^3) = 9\times(-1) \cdot x^{10+5} \cdot y^{3+3} = -9x^{15}y^6$$

Step2: Solve problem 11

Simplify coefficients, subtract exponents of like bases.
$$\frac{2d^7}{-4d^9d^5} = \frac{2}{-4} \cdot d^{7-(9+5)} = -\frac{1}{2}d^{-7} = \frac{1}{-2d^7} = -\frac{1}{2d^7}$$

Step3: Solve problem 12

Simplify coefficients, subtract exponents of like bases.
$$\frac{9x^{10}y^3}{-x^5y^3} = \frac{9}{-1} \cdot x^{10-5} \cdot y^{3-3} = -9x^5y^0 = -9x^5$$

Step4: Solve problem 15

Multiply exponents, convert to positive exponent.
$$(d^5)^{-2} = d^{5\times(-2)} = d^{-10} = \frac{1}{d^{10}}$$

Step5: Solve problem 16

Simplify power of power, multiply terms, convert to positive exponent.
$$(6x^3y)(x^2)^{-2} = (6x^3y)x^{2\times(-2)} = 6x^3y x^{-4} = 6x^{3-4}y = 6x^{-1}y = \frac{6y}{x}$$

Answer:

1. $\boldsymbol{-9x^{15}y^6}$
2. $\boldsymbol{-\frac{1}{2d^7}}$
3. $\boldsymbol{-9x^5}$
4. $\boldsymbol{\frac{1}{d^{10}}}$
5. $\boldsymbol{\frac{6y}{x}}$