Evaluate the Expression: Finding the Value of 2^7

Q: What's the difference between $ 2^7 $ and $ 2 \times 7 $ ?

Huge difference! $ 2^7 $ means 2 multiplied by itself 7 times (equals 128), while $ 2 \times 7 $ is just 2 times 7 (equals 14). The small raised number is an exponent, not a multiplication.

Q: Why isn't $ 2+2+2+2+2+2+2 $ the right answer?

That's addition, not multiplication! Exponents mean repeated multiplication, not repeated addition. $ 2^7 $ uses multiplication signs (×), not plus signs (+).

Q: Is there an easier way to calculate $ 2^7 $ ?

Yes! You can build up: $ 2^1 = 2 $, $ 2^2 = 4 $, $ 2^3 = 8 $, $ 2^4 = 16 $, $ 2^5 = 32 $, $ 2^6 = 64 $, $ 2^7 = 128 $. Each step doubles the previous result!

Q: What if I need to write out the multiplication for other bases?

Same rule applies! $ 3^4 $ becomes $ 3 \times 3 \times 3 \times 3 $, and $ 5^3 $ becomes $ 5 \times 5 \times 5 $. The exponent always tells you how many copies of the base to multiply together.

Exponential Notation with Repeated Multiplication

Choose the expression that is equal to the following:

$2^7$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's break down the expression.

00:08 Any number, M, to the power of 1 is just M itself.

00:13 Any number, M, to the power of 2 means M times M.

00:17 Any number, M, to the power of N means multiplying M by itself N times.

00:26 We'll use this formula in our exercise.

00:36 You'll see, it's like breaking down 2 multiplied by itself 7 times.

00:42 And that's how we solve this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the expression that is equal to the following:

$2^7$

Step-by-step solution

To solve this problem, we'll focus on expressing the power $2^7$ as a series of multiplications.

Step 1: Identify the given power expression $2^7$ .
Step 2: Convert $2^7$ into a product of repeated multiplication. This involves writing 2 multiplied by itself for a total of 7 times.
Step 3: The expanded form of $2^7$ is $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$ .

By comparing this expanded form with the provided choices, we see that the correct expression is:

$2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2$

Therefore, the solution to the problem is the expression that matches this expanded multiplication form, which is the choice $\text{1: } 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2$ .

Final Answer

$2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2$

Key Points to Remember

Essential concepts to master this topic

Definition: $a^n$ means base a multiplied by itself n times
Technique: $2^7 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
Check: Count the base factors: seven 2's multiplied together = $2^7$ ✓

Common Mistakes

Avoid these frequent errors

Confusing exponents with multiplication
Don't write $2^7 = 2 \times 7 = 14$ ! This confuses the exponent with a multiplication factor and gives completely wrong results. Always remember that the exponent tells you how many times to multiply the base by itself.

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

What's the difference between $2^7$ and $2 \times 7$ ?

Huge difference! $2^7$ means 2 multiplied by itself 7 times (equals 128), while $2 \times 7$ is just 2 times 7 (equals 14). The small raised number is an exponent, not a multiplication.

How do I remember what the exponent means?

Think of the exponent as "how many times do I write the base?" For $2^7$ , write the number 2 exactly 7 times with multiplication signs between them.

Why isn't $2+2+2+2+2+2+2$ the right answer?

That's addition, not multiplication! Exponents mean repeated multiplication, not repeated addition. $2^7$ uses multiplication signs (×), not plus signs (+).

Is there an easier way to calculate $2^7$ ?

Yes! You can build up: $2^1 = 2$ , $2^2 = 4$ , $2^3 = 8$ , $2^4 = 16$ , $2^5 = 32$ , $2^6 = 64$ , $2^7 = 128$ . Each step doubles the previous result!

What if I need to write out the multiplication for other bases?

Same rule applies! $3^4$ becomes $3 \times 3 \times 3 \times 3$ , and $5^3$ becomes $5 \times 5 \times 5$ . The exponent always tells you how many copies of the base to multiply together.

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Evaluate the Expression: Finding the Value of 2^7

Exponential Notation with Repeated Multiplication

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What's the difference between $2^7$ and $2 \times 7$ ?

How do I remember what the exponent means?

Why isn't $2+2+2+2+2+2+2$ the right answer?

Is there an easier way to calculate $2^7$ ?

What if I need to write out the multiplication for other bases?

🌟 Unlock Your Math Potential

More Questions

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Evaluate the Expression: Finding the Value of 10,000¹

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Evaluate the Expression: Finding the Value of 2^7

Exponential Notation with Repeated Multiplication

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What's the difference between 27 2^7 27 and 2×7 2 \times 7 2×7?

How do I remember what the exponent means?

Why isn't 2+2+2+2+2+2+2 2+2+2+2+2+2+2 2+2+2+2+2+2+2 the right answer?

Is there an easier way to calculate 27 2^7 27?

What if I need to write out the multiplication for other bases?

🌟 Unlock Your Math Potential

More Questions

Powers

Evaluate the Expression: Finding the Value of 10,000¹

Numerical Equality: Finding the Expression Equal to 100

Calculate the Area: Four x-cm Squares at y-cm Square Vertices

Solve the Equation: Finding the Exponent in -7^□ = -49

What's the difference between $2^7$ and $2 \times 7$ ?

Why isn't $2+2+2+2+2+2+2$ the right answer?

Is there an easier way to calculate $2^7$ ?