Mm,
How do you raise a
number in scientific
notation to a power?
A number writ t en in
sci en t i f i c no t at i o n i s a
product. Use the property
for raising a product to
a po wer.Raisin g a N u m b er in Scien t ific N o t at io n t o a Po w er
Aircraft The expression \mv2 gives the kinetic energy, in joules, of an object with a
mass of m kg traveling at a speed of v meters per second. What is the kinetic energy^
of an experimental unmanned jet with a mass of 1.3 x 103 kg traveling at a speed of
about 3.1 x 103 m/s?
Substitute the values for m
and v into the expression.
Rai se t h e t w o f ac t o r s t o t h e seco n d p o wer.
Multiply the exponents of a power raised to a power.
Use t he Co mmut at ive Propert y of M ul t i p l icat io n.
Add exponents of powers wit h the same base.
Si m p l i f y. W r i t e i n sc i e n t i f i c n o t a t i o n.l 2 1
2mv = 2
1
2
= 1
2
= 1
2
_ 1
2(1.3 X 103 )(3.1 X 10 3) 21.3 • 10 3 • 3.1 2 • (103) 2
1.3 • 10 3 • 3.1 2 • 10 6
1.3 • 3.1 2 • 10 3 • 10 6
1.3 • 3.1 2 • 103+6
6.2465 X 10s
The aircraft has a kinetic energy of about 6.2 X 10 joules.Go t It? 5. What is the kinetic energy of an aircraft with a mass of 2.5 X 105 kg traveling
at a speed of 3 X 102 m/s?Lesso n Ch eck
Do yo u k n o w H OW?
Simplify each expression.
1. (n3) 6 2. (b-7)3- (3fl^)4 4. (9x5)2(x2)5
Simplify each expression. Write each answer in
scientific notation.- (4 X 10 5) 2 6. (2 X 1(T3)5
\
_ /{^MATHEMATICAL
Do yo u UN DERSTAN D? PRA CTICES
^ 7. Vocabulary Compare and contrast the property
for raising a power to a power and the property for
multiplying powers with the same base.
@ 8. Er r o r A n al y si s One student simplified x 5 + x 5 to
x10. A second student simplified x 5 + x 5 to 2x5.
Which student is correct? Explain.
^ 9. Open-Ended Write four different expressions that are
equivalent to (x^)3.Pr act i cePr act i ce an d Pr o b l em - So l v i n g Ex er ci ses
Simplify each expression.10. (n8) 4 11. (n4) 8- (u/7)-1 1 5. (xi)“5
- («i) 3 c 4 19. (c 3 )5(d3)°
MATHEMATICAL
PRA CTICES12. (c2)J- d (r T2)“ 9
20. {t2T \ t2r 5Se e Pr o b l e m s 1 an d 2.- (xt)10
- (z8)°Z2
21. (m 3 )_ 1 (x5)J436 Ch a p t e r 7 Ex p o n e n t s a n d Ex p o n e n t i a l Fu n c t i o n s