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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.2, Problem 2E

(a)

To determine

**To fill: “**The blank in the statement “When we multiply two powers with the same base, we _____ the exponents. So

Expert Solution

The complete statement is “When we multiply two powers with the same base, we

The given expression is

**Formula used:**

“The product of two powers with the same base *a* and different exponents *m* and *n* is given by,

That is, while multiplying two powers with same base, the exponents are added and the base will remain the same.

**Calculation:**

The given statement is “When we multiply two powers with the same base, we _____ the exponents. So

By the above mentioned formula, it can be clearly noted that while multiplying two powers with the same base, the exponents are added.

Now, consider the given expression

Compare the given expression *a*, *m* and *n* as shown below.

Note that,

Substitute

Thus, the value for the expression

Therefore, the complete statement is “When we multiply two powers with the same base, we

(b)

To determine

**To fill: “**The blank in the statement “When we divide two powers with the same base, we _____ the exponents. So

Expert Solution

The complete statement is “When we divide two powers with the same base, we

The given expression is

**Formula used:**

“The division of two powers with the same base *a* and different exponents *m* and *n* is given by,

That is, while dividing two powers with same base, the exponents are subtracted and the base will remain the same.

**Calculation:**

The given statement is “When we divide two powers with the same base, we _____ the exponents. So

By the above mentioned formula, it can be clearly noted that while dividing two powers with the same base, the exponents are subtracted.

Now, consider the given expression

Compare the given expression *a*, *m* and *n* as shown below.

Note that,

Substitute

Thus, the value for the expression

Therefore, the complete statement is “When we divide two powers with the same base, we