SOPHIA ALGEBRA UNIT 1
MILESTONE 1
, You passed this Milestone
17 questions were answered correctly.
4 questions were answered incorrectly.
1
Write the expression as a single power of b.
RATIONALE
Start by simplifying the terms in the parentheses. Using
the Quotient Property of Exponents, divide the two
terms that have the same base by subtracting the
exponents, and .
When subtracting fractions, make sure that the
denominators are the same. For this question, you can
, make both denominators 4, so you only need to change
the first fraction. To do this, multiply both the
numerator and denominator by 2.
Now that there are common denominators, we can
subtract the numerators while keeping the denominator
the same.
minus equals . Next, apply the Power
Property of Exponents to multiply the two
exponents, and , to write b as a single power.
times equals . The simplified expression is
.
CONCEPT
Properties of Fractional and Negative Exponents
2
The speed of light is approximately 299,000,000 meters per
second.
What is the speed of the light, in meters per second, using
scientific notation?
meters per second
meters per second
,
meters per second
meters per second
RATIONALE
To express this number in scientific notation, you must
find two parts: a number between one and ten (it can be
equal to one, but not ten), and a power of 10. To find the
first part, place the decimal after the first non-zero
number, 2.
The decimal will be placed after the 2. We will also
include the numbers right after the 2, which were
99. These will go immediately after the decimal. To find
the second part, you must find the exponent to which 10
will be raised. To do this, count how many times the
decimal is moved from 2.99 to obtain 299,000,000.
If we start with the decimal right after the 2, it would
take us eight moves to the right to obtain the original
number. Because we must move the decimal point eight
times, the exponent is 8.
Combine the two parts to state the solution in scientific
notation. The speed of light is approximately meters
per second.
CONCEPT
MILESTONE 1
, You passed this Milestone
17 questions were answered correctly.
4 questions were answered incorrectly.
1
Write the expression as a single power of b.
RATIONALE
Start by simplifying the terms in the parentheses. Using
the Quotient Property of Exponents, divide the two
terms that have the same base by subtracting the
exponents, and .
When subtracting fractions, make sure that the
denominators are the same. For this question, you can
, make both denominators 4, so you only need to change
the first fraction. To do this, multiply both the
numerator and denominator by 2.
Now that there are common denominators, we can
subtract the numerators while keeping the denominator
the same.
minus equals . Next, apply the Power
Property of Exponents to multiply the two
exponents, and , to write b as a single power.
times equals . The simplified expression is
.
CONCEPT
Properties of Fractional and Negative Exponents
2
The speed of light is approximately 299,000,000 meters per
second.
What is the speed of the light, in meters per second, using
scientific notation?
meters per second
meters per second
,
meters per second
meters per second
RATIONALE
To express this number in scientific notation, you must
find two parts: a number between one and ten (it can be
equal to one, but not ten), and a power of 10. To find the
first part, place the decimal after the first non-zero
number, 2.
The decimal will be placed after the 2. We will also
include the numbers right after the 2, which were
99. These will go immediately after the decimal. To find
the second part, you must find the exponent to which 10
will be raised. To do this, count how many times the
decimal is moved from 2.99 to obtain 299,000,000.
If we start with the decimal right after the 2, it would
take us eight moves to the right to obtain the original
number. Because we must move the decimal point eight
times, the exponent is 8.
Combine the two parts to state the solution in scientific
notation. The speed of light is approximately meters
per second.
CONCEPT
