Math / Numbers & Operations

QuestionWhat is the value of a power if the exponent is 0 ? We can use patterns to find out. Let's look at powers of 3. Notice that as we decrease the exponent of 3 by 1 , we divide the product by 3 . $\begin{array}{l} 3^{4}=81 \\ 3^{3}=27\left\{\begin{array} { l } { \div 3 } \\ { 3 ^ { 2 } = } \\ { 3 ^ { 1 } = - } \\ { 3 ^ { 0 } = } \end{array} \left\{\begin{array}{l} \div 3 \\ \div 3 \end{array}\right.\right. \end{array}$

Studdy Solution

STEP 1

What is this asking? What happens when a number is raised to the power of zero? Watch out! It's tempting to think anything to the zero power is zero, but that's a trap!

STEP 2

1. Establish the pattern.
2. Extend the pattern.

STEP 3

Alright, let's break this down!
We're given $3^4 = 81$ .
Then, $3^3 = 27$ , which is $81 \div 3$ .
See what's happening?
Each time we lower the exponent by one, we divide the result by three, the base of the exponent!

STEP 4

Let's confirm the pattern.
We have $3^3 = 27$ .
If we divide by three, we get $27 \div 3 = 9$ , which is indeed $3^2 = 9$ .
So, our pattern holds!

STEP 5

Now, let's continue the pattern.
We have $3^2 = 9$ .
Dividing by three gives us $9 \div 3 = 3$ , which is $3^1 = 3$ .
Awesome!

STEP 6

Keep it going!
We have $3^1 = 3$ .
Dividing by three gives us $3 \div 3 = 1$ .
So, following the pattern, we find that $3^0 = 1$ !

STEP 7

Following the pattern of dividing by three as we decrease the exponent, we find that $3^0 = 1$ .

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Studdy Solution

STEP 1

What is this asking? What happens when a number is raised to the power of zero? Watch out! It's tempting to think anything to the zero power is zero, but that's a trap!

STEP 2

1. Establish the pattern.
2. Extend the pattern.

STEP 3

Alright, let's break this down!
We're given $3^4 = 81$ .
Then, $3^3 = 27$ , which is $81 \div 3$ .
See what's happening?
Each time we lower the exponent by one, we divide the result by three, the base of the exponent!

STEP 4

Let's confirm the pattern.
We have $3^3 = 27$ .
If we divide by three, we get $27 \div 3 = 9$ , which is indeed $3^2 = 9$ .
So, our pattern holds!

STEP 5

Now, let's continue the pattern.
We have $3^2 = 9$ .
Dividing by three gives us $9 \div 3 = 3$ , which is $3^1 = 3$ .
Awesome!

STEP 6

Keep it going!
We have $3^1 = 3$ .
Dividing by three gives us $3 \div 3 = 1$ .
So, following the pattern, we find that $3^0 = 1$ !

STEP 7

Following the pattern of dividing by three as we decrease the exponent, we find that $3^0 = 1$ .

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Studdy Solution

STEP 1

What is this asking? What happens when a number is raised to the power of zero? Watch out! It's tempting to think anything to the zero power is zero, but that's a trap!

STEP 2

1. Establish the pattern.2. Extend the pattern.

STEP 3

Alright, let's break this down!We're given 34=813^4 = 8134=81.Then, 33=273^3 = 2733=27, which is 81÷381 \div 381÷3.See what's happening?Each time we lower the exponent by **one**, we divide the result by **three**, the **base** of the exponent!

STEP 4

Let's confirm the pattern.We have 33=273^3 = 2733=27.If we divide by **three**, we get 27÷3=927 \div 3 = 927÷3=9, which is indeed 32=93^2 = 932=9.So, our pattern holds!

STEP 5

Now, let's continue the pattern.We have 32=93^2 = 932=9.Dividing by **three** gives us 9÷3=39 \div 3 = 39÷3=3, which is 31=33^1 = 331=3.Awesome!

STEP 6

Keep it going!We have 31=33^1 = 331=3.Dividing by **three** gives us 3÷3=13 \div 3 = 13÷3=1.So, following the pattern, we find that 30=13^0 = 130=1!

STEP 7

Following the pattern of dividing by three as we decrease the exponent, we find that 30=13^0 = 130=1.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Establish the pattern.
2. Extend the pattern.

Alright, let's break this down!
We're given $3^4 = 81$ .
Then, $3^3 = 27$ , which is $81 \div 3$ .
See what's happening?
Each time we lower the exponent by one, we divide the result by three, the base of the exponent!

Let's confirm the pattern.
We have $3^3 = 27$ .
If we divide by three, we get $27 \div 3 = 9$ , which is indeed $3^2 = 9$ .
So, our pattern holds!

Now, let's continue the pattern.
We have $3^2 = 9$ .
Dividing by three gives us $9 \div 3 = 3$ , which is $3^1 = 3$ .
Awesome!

Keep it going!
We have $3^1 = 3$ .
Dividing by three gives us $3 \div 3 = 1$ .
So, following the pattern, we find that $3^0 = 1$ !

Following the pattern of dividing by three as we decrease the exponent, we find that $3^0 = 1$ .