Concept explainers
a.
To find which pair of expressions are equivalent.
a.
Answer to Problem 7.1.3P
Not equivalent
Explanation of Solution
Given:
Formula used:
aman = am + n for a ≠ 0 or m , n ≥ 0;
Calculation:
Left hand side,
Using identity and substituting value,
=
Solving,
=
Right hand side,
=
Solving,
=
So, using identity ( am ) n = amn for a ≠ 0 or m ≥ 0;
=(2)21
Hence, left hand side
b.
To find which pair of expressions are equivalent.
b.
Answer to Problem 7.1.3P
Equivalent
Explanation of Solution
Given:
Formula used:
aman = am + n for a ≠ 0 or m , n ≥ 0;
Calculation:
Left hand side,
Using identity and substituting value,
=
Solving,
=
Right hand side,
=
Hence, left hand side= right hand side.
c.
To find which pair of expressions are equivalent.
c.
Answer to Problem 7.1.3P
Equivalent
Explanation of Solution
Given:
Formula used:
aman = am + n for a ≠ 0 or m , n ≥ 0;
Calculation:
Left hand side,
Putting all like terms together,
Using identity and substituting value,
=
Solving,
=
Right hand side,
=
Hence, left hand side=right hand side.
d.
To find which pair of expressions are equivalent.
d.
Answer to Problem 7.1.3P
Not equivalent
Explanation of Solution
Given:
Formula used:
aman = am + n for a ≠ 0 or m , n ≥ 0;
( am ) n = amn for a ≠ 0 or m ≥ 0;
Calculation:
Left hand side,
Using identity and substituting value,
=
Solving,
=
So,
=
And,
=
Right hand side,
=
Hence, left hand side
e.
To find which pair of expressions are equivalent.
e.
Answer to Problem 7.1.3P
Equivalent
Explanation of Solution
Given:
Formula used:
( am ) n = amn for a ≠ 0 or m ≥ 0;
Calculation:
Left hand side,
Using identity and substituting value,
=
Solving,
=
So,
=
Right hand side,
Using identity and substituting value,
=
Solving,
=
So,
=
Hence, left hand side=right hand side.
f.
To find which pair of expressions are equivalent.
f.
Answer to Problem 7.1.3P
Equivalent
Explanation of Solution
Given:
Formula used:
( am ) n = amn for a ≠ 0 or m ≥ 0;
Calculation:
Left hand side,
Using identity and substituting value,
=
Solving,
=
So,
=
And,
=
Right hand side,
Using identity and substituting value,
=
Solving,
=
So,
=
=
Hence, left hand side=right hand side.
Chapter ISG Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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