QuestionCalculate $(-5)^{17}=$

Studdy Solution

STEP 1

Assumptions1. We are multiplying -5 by itself17 times.

STEP 2

We need to understand the properties of multiplication of negative numbers. The product of two negative numbers is a positive number. $(-a) \times (-b) = a \times b$

STEP 3

If we multiply -5 by itself an even number of times, the result will be positive because the product of two negative numbers is a positive number.
$(-5) \times (-5) =25$

STEP 4

If we multiply - by itself an odd number of times, the result will be negative because the product of a negative number and a positive number is a negative number.
$(-) \times25 = -125$

STEP 5

In our case, we are multiplying -5 by itself17 times. Since17 is an odd number, the result will be negative.

STEP 6

We can simplify the problem by first calculating the result of multiplying -5 by itself16 times (an even number), and then multiplying that result by -5.
$(-5) \times \cdots \times(-5)_{16 \text { times }} \times -5$

STEP 7

Calculate the result of multiplying -5 by itself16 times.
$(-5) \times \cdots \times(-5)_{16 \text { times }} =5^{16}$

STEP 8

Now, multiply the result by -5.
$5^{16} \times -5$

STEP 9

Calculate the result.
$5^{16} \times -5 = -5^{17}$ The result of multiplying -5 by itself17 times is $-5^{17}$ .

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