Warm Up Find the product. 62 5 1. 5 • 5 • 5 • 5 2. 3 • 3 • 3 3. (–7) • (–7) • (–7) 4. 9 • 9 27 – 343 81
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Warm UpFind the product.
6251. 5 • 5 • 5 • 52. 3 • 3 • 3
3. (–7) • (–7) • (–7)
4. 9 • 9
27
–343
81
If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. A number produced by raising a base to an exponent is called a power. Both 27 and 33 represent the same power.
7
ExponentBase
2
Identify how many times 4 is a factor.4 • 4 • 4 • 4 = 44
Write in exponential form.
A. 4 • 4 • 4 • 4
Read (–63) as “6 to the 3rd power or 6 cubed”.
Reading Math
Identify how many times –6 is a factor.(–6) • (–6) • (–6) = (–6)3
B. (–6) • (–6) • (–6)
(–6)2 is not the same thing as -62! (–6)2 = 36. -62 = -36
Very Important Math
Identify how many times 5 and d are used as a factor.
C. 5 • 5 • d • d • d • d
Write in exponential form.
5 • 5 = 52d4
NEGATIVE EXPONENTS
The reciprocal of a number is 1 divided by that number.
Remember!
Negative Exponents
5–3
Write the reciprocal; change the sign of the exponent.
Evaluate.
Find the product of three ’s.1 5
Simplify.
51 3
=
15 • 5 • 5
=
1251
=
(–10)–3
Write the reciprocal; change the sign of the exponent.
Evaluate.
Find the product of three ’s. 1 –10
Simplify.
1 = –10
3
1–10 • –10 • –10
=
–1000 1
= = –0.001
The Zero Power
Any number (except 0) raised to the zero power is equal to 1.
1490 = 1
Subtract inside the parentheses.
Evaluate 5 – (6 – 4)–3 + (– 2)0.
Evaluate the exponents.
5 – (6 – 4)–3 + (–2)0
= 5 – (2)–3 + (–2)0
= 5 – + 1 1 8
= 5 7 8
Add and subtract from left to right.
Did you know?
Any number raised to the first power is always equal to itself. 81 = 8
If a number is raised to the second power, we say it is squared. 32 is read as three squared.
If a number is raised to the third power, we say it is cubed. 43 is read as four cubed.
I Love Exponents!
It’s Hip to be Square!
Lesson Quiz: Part I
Write in exponential form.
1. n • n • n • n
2. (–8) • (–8) • (–8) • (h)
256
–213
(–8)3h
3. Evaluate (–4)4
4. Evaluate x • z – yx for x = 5, y = 3, and z = 6.
4n
5. Evaluate (2/3)-3 27/8
5. A population of bacteria doubles in size every minute. The number of bacteria after 5 minutes is 15 25. How many are there after 5 minutes?
Lesson Quiz: Part II
480
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