# “ The blank in the statement “When we multiply two powers with the same base, we _____ the exponents. So 3 4 ⋅ 3 5 = _ _ _ ”.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

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 34⋅35=___”.

Expert Solution

The complete statement is “When we multiply two powers with the same base, we Add_ the exponents. So 3435=39_”.

### Explanation of Solution

The given expression is 3435.

Formula used:

“The product of two powers with the same base a and different exponents m and n is given by, aman=am+n”.

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 3435=___”.

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 3435.

Compare the given expression 3435 with the expression aman=am+n and obtain the values of a, m and n as shown below.

Note that, a=3,m=4,n=5.

Substitute a=3,m=4,n=5 in aman=am+n and simplify as shown below.

aman=am+n3435=34+53435=39

Thus, the value for the expression 3435 is 39.

Therefore, the complete statement is “When we multiply two powers with the same base, we Add_ the exponents. So 3435=39_”.

(b)

To determine

### To fill: “The blank in the statement “When we divide two powers with the same base, we _____ the exponents. So 3532=___”.

Expert Solution

The complete statement is “When we divide two powers with the same base, we Subtract_ the exponents. So 3532=33_”.

### Explanation of Solution

The given expression is 3532.

Formula used:

“The division of two powers with the same base a and different exponents m and n is given by, aman=amn”.

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 3532=___”.

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 3532.

Compare the given expression 3532 with the expression aman=amn and obtain the values of a, m and n as shown below.

Note that, a=3,m=5,n=2.

Substitute a=3,m=5,n=2 in aman=amn and simplify as shown below.

aman=amn3532=3523532=33

Thus, the value for the expression 3532 is 33.

Therefore, the complete statement is “When we divide two powers with the same base, we Subtract_ the exponents. So 3532=33_”.

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