9.1 Exponents

Practice Journal Page (no calculators)

A power is an expression written with an exponent and a base or the value of such an expression. 3² is an example of a power. The base is the number that is used as a factor. 3 2 The exponent, 2 tells how many times the base, 3, is used as a factor.

When a number is raised to the second power, we usually say it is “squared.” The area of a square is s  s = s 2, is the side length. S S When a number is raised to the third power, we usually say it is “cubed.” The of volume of a cube is s  s  s = s 3 is the side length. S S S

Write the power represented by the geometric model The figure is 5 units long, 5 units wide, and 5 units tall. 5  5  5 The factor 5 is used 3 times. 5353

Write the power represented by the geometric model. x x

There are no easy geometric models for numbers raised to exponents greater than 3, but you can still write them using repeated multiplication or a base and exponent. 3 to the second power, or 3 squared 3  3  3  3  3 MultiplicationPowerValueWords 3  3  3  3 3  3  3 3  to the first power 3 to the third power, or 3 cubed 3 to the fourth power 3 to the fifth power Reading Exponents

Caution! In the expression –5 2, 5 is the base because the negative sign is not in parentheses. In the expression (–2), –2 is the base because of the parentheses.

Evaluate each expression. A. (–6) 3 (–6)(–6)(–6) –216 B. –10 2 – –100 Use –6 as a factor 3 times. Find the product of –1 and two 10’s. Think of a negative sign in front of a power as multiplying by a –1.

Use as a factor 2 times Evaluate the expression. C  2929 =  2929

Evaluate each expression. a. (–5) 3 b. –6 2

Evaluate the expression. c.

Write each number as a power of the given base. A. 64; base 8 8  B. 81; base –3 (–3)(–3)(–3)(–3) (–3) 4 The product of two 8’s is 64. The product of four –3’s is 81.

Write each number as a power of a given base. a. 64; base 4 b. –27; base –3