Powers & Roots When we say an integer or real number is “raised to a power”, we are talking about exponents.

Powers & Roots When we say an integer or real number is “raised to a power”, we are talking about exponents. Exponents appear as a small number superscripted above a base.

Powers & Roots 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡 When we say an integer or real number is “raised to a power”, we are talking about exponents. Exponents appear as a small number superscripted above a base. 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡

Powers & Roots 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡 When we say an integer or real number is “raised to a power”, we are talking about exponents. Exponents appear as a small number superscripted above a base. 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡 Here are some examples : 3 2 , (−4) 3 , 2 5

Powers & Roots 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡 When we say an integer or real number is “raised to a power”, we are talking about exponents. Exponents appear as a small number superscripted above a base. 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡 Here are some examples : 3 2 , (−4) 3 , 2 5 To evaluate these numbers, we take the base, and then multiply that base the number of times given by the exponent.

Powers & Roots 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡 When we say an integer or real number is “raised to a power”, we are talking about exponents. Exponents appear as a small number superscripted above a base. 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡 Here are some examples : 3 2 , (−4) 3 , 2 5 To evaluate these numbers, we take the base, and then multiply that base the number of times given by the exponent. For example : 2 3 =2×2×2 ( take your base 2 and multiply it three times )

Powers & Roots 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡 When we say an integer or real number is “raised to a power”, we are talking about exponents. Exponents appear as a small number superscripted above a base. 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡 Here are some examples : 3 2 , (−4) 3 , 2 5 To evaluate these numbers, we take the base, and then multiply that base the number of times given by the exponent. For example : 2 3 =2×2×2 ( take your base 2 and multiply it three times ) (−4) 4 =(−4)×(−4)×(−4)×(−4)

Powers & Roots An easier way to evaluate these is by use of a calculator. The ^ button on the calculator is located above the 𝑥 2 button.

Powers & Roots An easier way to evaluate these is by use of a calculator. The ^ button on the calculator is located above the 𝑥 2 button. EXAMPLES : Using a calculator evaluate 2 3 Press 2 , ^ , 3 , = answer is 8

Powers & Roots An easier way to evaluate these is by use of a calculator. The ^ button on the calculator is located above the 𝑥 2 button. EXAMPLES : Using a calculator evaluate 2 3 Press 2 , ^ , 3 , = answer is 8 3 5 Press 3 , ^ , 5 , = answer is 243

Powers & Roots An easier way to evaluate these is by use of a calculator. The ^ button on the calculator is located above the 𝑥 2 button. EXAMPLES : Using a calculator evaluate 2 3 Press 2 , ^ , 3 , = answer is 8 3 5 Press 3 , ^ , 5 , = answer is 243 (−4) 2 Press ( , - , 4 , ) , ^ , 2 , = answer is 16

Powers & Roots We will also be using roots in our work. A root of a number is a quantity that is taken two or more times as an equal factor of the number.

Powers & Roots We will also be using roots in our work. A root of a number is a quantity that is taken two or more times as an equal factor of the number. The symbol for a root 𝑖𝑛𝑑𝑒𝑥 𝑏𝑎𝑠𝑒 has some base under what is called a “radical”. The root taken is understood to be a 2, unless otherwise shown by the index. If there is no index shown, we take the square root ( index = 2 )

Powers & Roots EXAMPLES : 4 , 25 , 3 8 We will also be using roots in our work. A root of a number is a quantity that is taken two or more times as an equal factor of the number. The symbol for a root 𝑖𝑛𝑑𝑒𝑥 𝑏𝑎𝑠𝑒 has some base under what is called a “radical”. The root taken is understood to be a 2, unless otherwise shown by the index. If there is no index shown, we take the square root ( index = 2 ) EXAMPLES : 4 , 25 , 3 8

Powers & Roots EXAMPLES : 4 , 25 , 3 8 We will also be using roots in our work. A root of a number is a quantity that is taken two or more times as an equal factor of the number. The symbol for a root 𝑖𝑛𝑑𝑒𝑥 𝑏𝑎𝑠𝑒 has some base under what is called a “radical”. The root taken is understood to be a 2, unless otherwise shown by the index. If there is no index shown, we take the square root ( index = 2 ) EXAMPLES : 4 , 25 , 3 8 ** warning – you CAN NOT take an even indexed root of a negative value.

Powers & Roots I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed.

Powers & Roots I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed. Above the 𝑥 2 button in blue you will find the square root button.

Powers & Roots I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed. Above the 𝑥 2 button in blue you will find the square root button. To evaluate 100 you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , =

Powers & Roots I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed. Above the 𝑥 2 button in blue you will find the square root button. To evaluate 100 you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , = ANSWER = 10

Powers & Roots I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed. Above the 𝑥 2 button in blue you will find the square root button. To evaluate 100 you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , = ANSWER = 10 To evaluate 12 you enter 2nd , 𝑥 2 , 12 , =

Powers & Roots I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed. Above the 𝑥 2 button in blue you will find the square root button. To evaluate 100 you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , = ANSWER = 10 To evaluate 12 you enter 2nd , 𝑥 2 , 12 , = ANSWER = 3.464 ( rounded )

Powers & Roots I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed. Above the 𝑥 2 button in blue you will find the square root button. To evaluate 100 you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , = ANSWER = 10 To evaluate 12 you enter 2nd , 𝑥 2 , 12 , = ANSWER = 3.464 ( rounded ) Above the ^ button is the nth root button 𝑥

Powers & Roots I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed. Above the 𝑥 2 button in blue you will find the square root button. To evaluate 100 you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , = ANSWER = 10 To evaluate 12 you enter 2nd , 𝑥 2 , 12 , = ANSWER = 3.464 ( rounded ) Above the ^ button is the nth root button It will calculate any root greater than 2. 𝑥

Powers & Roots I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed. Above the 𝑥 2 button in blue you will find the square root button. To evaluate 100 you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , = ANSWER = 10 To evaluate 12 you enter 2nd , 𝑥 2 , 12 , = ANSWER = 3.464 ( rounded ) Above the ^ button is the nth root button It will calculate any root greater than 2. To evaluate 3 8 you enter 3 , 2nd , ^ , 8 , = 𝑥

Powers & Roots I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed. Above the 𝑥 2 button in blue you will find the square root button. To evaluate 100 you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , = ANSWER = 10 To evaluate 12 you enter 2nd , 𝑥 2 , 12 , = ANSWER = 3.464 ( rounded ) Above the ^ button is the nth root button It will calculate any root greater than 2. To evaluate 3 8 you enter 3 , 2nd , ^ , 8 , = ANSWER is 2 𝑥

Powers & Roots I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed. Above the 𝑥 2 button in blue you will find the square root button. To evaluate 100 you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , = ANSWER = 10 To evaluate 12 you enter 2nd , 𝑥 2 , 12 , = ANSWER = 3.464 ( rounded ) Above the ^ button is the nth root button It will calculate any root greater than 2. To evaluate 3 8 you enter 3 , 2nd , ^ , 8 , = ANSWER is 2 To evaluate 4 10 you enter 4 , 2nd , ^ , 10 , = 𝑥

Powers & Roots I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed. Above the 𝑥 2 button in blue you will find the square root button. To evaluate 100 you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , = ANSWER = 10 To evaluate 12 you enter 2nd , 𝑥 2 , 12 , = ANSWER = 3.464 ( rounded ) Above the ^ button is the nth root button It will calculate any root greater than 2. To evaluate 3 8 you enter 3 , 2nd , ^ , 8 , = ANSWER is 2 To evaluate 4 10 you enter 4 , 2nd , ^ , 10 , = ANSWER is 1.778 ( rouned ) 𝑥