Exponent Worksheet Page 2
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1
216. Write each of the following expression in equivalent exponential form. For those involving negative
exponents, write an equivalent form without using negative exponents. For those involving positive
exponents, write an equivalent form using negative exponents.
1
4
2
1
1
2
a)
4
5 .
b)
7
x
c)
d)
5
5
2
2
5
2
3
e)
5
x
f)
g)
4
ax
h)
3
5
t
22. When very large numbers are using in scientific work, they are usually written in what is called
scientific notation – that is, as the product of a decimal between 1 and 10 with some power of 10. For
example, basic measurements of the Earth are often given in scientific notation like this:
Measurement
Standard Form
Scientific Notation
Land Area (in m²)
58,969,045,000,000
13
. 5
897
10
Volume (in km³)
1,083,000,000,000,000,000
18
. 1
083
10
Population
6,214,891,000
9
. 6
215
10
Mass (in kg)
5,976,000,000,000,000,000,000,000
24
. 5
976
10
a)
Write each of these large numbers in scientific notation rounded to three decimal places.
i)
234,567,890
ii)
54,987
iii)
1,024,456,981,876
b)
Use negative exponents to write each of these numbers in scientific notation.
i)
0.0234
ii)
0.00002056
iii)
0.000000000008
c)
Translate each of these numbers, given in scientific notation, to standard numeral form.
8
6
3
i)
. 7
82
10
ii)
. 5
032
10
iii)
8
1 .
10
d)
Express the results of these calculations in scientific notation, without using a calculator.
Be prepared to explain your reasoning and how you use properties of exponents to reach
the results.
12
5
12
5
12
5
i)
4
10
3
10
ii)
40
10
5
10
iii)
4
10
3
10
30. A student at Sam Houston High School in Texas wrote the following equations to show equivalence
of exponential forms. Decide which of the statements are correct. Correct those that are incorrect by
revising the right side of the given equations. Give the student advice for correct thinking about the
indicated calculations.
2
3
3
x
30
x
y
2
3
3
a)
x
b)
2
x
x
3
x
c)
24
x
y
3
6
xy
x
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