(a).
To find: The four different ways to write the given expression as a product of two powers with the same base using positive exponents.
(a).
Answer to Problem 46PPE
The four different ways to write the given expression as a product of two powers with the same base are
Explanation of Solution
Given information:
The given expression is
Calculation:
Formula for the property of addition of exponents for any positive integer
The given expression can be written in the first way as:
Apply the addition property of exponents raise to a power in the above expression.
The given expression can be written in the second way as:
Apply the addition property of exponents raise to a power in the above expression.
The given expression can be written in the third way as:
Apply the addition property of exponents raise to a power in the above expression.
The given expression can be written in the fourth way as:
Apply the addition property of exponents raise to a power in the above expression.
Therefore, the four different ways to write the given expression as a product of two powers with the same base are
(b).
To find: The four different ways to write the given expression as a product of two powers with the same base using negative or zero exponents in each product.
(b).
Answer to Problem 46PPE
The four different ways to write the given expression as a product of two powers with the same base ding zero exponents are
Explanation of Solution
Given information:
The given expression is
Calculation:
Formula for the property of addition of exponents for any positive integer
The given expression can be written in the first way as:
Apply the addition property of exponents raise to a power in the above expression.
The given expression can be written in the second way as:
Apply the addition property of exponents raise to a power in the above expression.
The given expression can be written in the third way as:
Apply the addition property of exponents raise to a power in the above expression.
The given expression can be written in the fourth way as:
Apply the addition property of exponents raise to a power in the above expression.
So, the four different ways to write the given expression as a product of two powers with the same base using zero exponents are
For negative exponents, the expression can be written as:
Express the given expression using the above formula is:
First way:
Second way:
Third way:
Fourth way:
So, the four different ways to write the given expression as a product of two powers with the same base using negative exponents are
Therefore, the four different ways to write the given expression as a product of two powers with the same base ding zero exponents are
(c).
To find: The reason and different number of ways to write the given expression as a product of two powers.
(c).
Explanation of Solution
Given information:
The given expression is
Reason:
As calculated in part (a) and (b), the given expression can be written as positive, negative and zero exponents in four different ways each. However, the exponents can be infinitely large in numbers for negative exponents as the power
Chapter 7 Solutions
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
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