Exponents and Equivalent Expressions

​Product of Powers Exponent Law When multiplying two powers that have the same nonzero base, ADD the exponents and keep the same base.

Open Ended

$$\left(-\frac{1}{3}\right)^2\left(-\frac{1}{3}\right)^3$$  

​Power of a Power Exponent Law When raising a base with a power to another power, MULTIPLY the exponents and keep the same base.

Multiple Choice

Evaluate the numerical expression by using Laws of Exponents.

$$\left(\left(-2\right)^2\right)^3$$  

• 12

• -12

• 64

• -64

​When dividing two powers that have the same nonzero base, keep the base and SUBTRACT the exponents. This is called the quotient of powers exponent law.

Multiple Choice

Simplify the expression.

$$\frac{\left(-3.1\right)^7}{\left(-3.1\right)^5}$$  

• $$\left(-3.1\right)^2$$  

• $$\left(-3.1\right)^{12}$$  

• $$\left(-3.1\right)^{35}$$  

• $$\left(-3.1\right)^0$$  

​When a nonzero real number is raised to the zero power, its value equals ONE. This is called the zero exponent law.

Open Ended

What is the value of the expression?

$$\frac{4^2\times3^0}{1^5}$$  

​Order of Operations

​Grouping Symbols

Exponents

Multiplication/Division

Addition/Subtraction​

Open Ended

What is the value of the expression?

$$\left(\left|3.9-5.9\right|-\left(-2.5\right)\right)^2$$  

Open Ended

What is the value of the expression?

$$\left(2.5\right)^1\left(2\right)^4$$