Calculate 7² as an Integer: Converting Power to Standard Form

Q: What does the little 2 above the 7 mean?

The small 2 is called an exponent or power. It tells you how many times to multiply the base number (7) by itself. So $ 7^2 $ means 7 times 7.

Q: Is there a pattern to help me remember perfect squares?

Yes! Try memorizing the first 12 perfect squares: $ 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36, 7^2=49, 8^2=64, 9^2=81, 10^2=100 $. Notice how they grow quickly!

Q: How do I check if my answer is correct?

Ask yourself: 'What number times itself equals my answer?' For 49, think: $ \sqrt{49} = 7 $. Since 7 × 7 = 49, your answer is right!

Q: What if I see 7³ instead of 7²?

That would be 7 cubed, meaning $ 7 \times 7 \times 7 = 343 $. The exponent tells you exactly how many 7s to multiply together.

Exponent Evaluation with Perfect Squares

Write the following as an integer:

$7^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's use the power formula

00:06 Any number (X) to the power of (N)

00:09 equals X multiplied by itself N times

00:17 Let's use this formula in our exercise

00:22 Let's break down the power into multiplications

00:29 Let's calculate the multiplications

00:32 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the following as an integer:

$7^2=$

Step-by-step solution

To solve this problem, we need to evaluate the expression $7^2$ . This expression means $7$ multiplied by itself, due to the exponent $2$ .

Step 1: Identify the base and exponent — here the base is $7$ and the exponent is $2$ .
Step 2: Apply the definition of exponents: calculate $7 \times 7$ .

Now, let's perform the calculation:

$7 \times 7 = 49$ .

Therefore, the integer value of $7^2$ is $\textbf{49}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: An exponent of 2 means multiply base by itself
Technique: Calculate $7^2 = 7 \times 7 = 49$
Check: Verify that 49 is indeed 7 multiplied by itself ✓

Common Mistakes

Avoid these frequent errors

Multiplying base by exponent instead of applying exponent rule
Don't calculate 7 × 2 = 14! This confuses multiplication with exponentiation and gives completely wrong results. Always remember that exponents mean repeated multiplication: 7² means 7 × 7, not 7 × 2.

Practice Quiz

Test your knowledge with interactive questions

Which of the following is equivalent to the expression below?

$$ $$ 10,000^1 $$

FAQ

Everything you need to know about this question

What does the little 2 above the 7 mean?

The small 2 is called an exponent or power. It tells you how many times to multiply the base number (7) by itself. So $7^2$ means 7 times 7.

Why is 7² called 'seven squared'?

It's called 'squared' because when you arrange 7 × 7 = 49 objects in a square pattern, you get 7 rows and 7 columns. Perfect squares like 1, 4, 9, 16, 25, 36, 49 all come from squaring whole numbers!

Is there a pattern to help me remember perfect squares?

Yes! Try memorizing the first 12 perfect squares: $1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36, 7^2=49, 8^2=64, 9^2=81, 10^2=100$ . Notice how they grow quickly!

How do I check if my answer is correct?

Ask yourself: 'What number times itself equals my answer?' For 49, think: $\sqrt{49} = 7$ . Since 7 × 7 = 49, your answer is right!

What if I see 7³ instead of 7²?

That would be 7 cubed, meaning $7 \times 7 \times 7 = 343$ . The exponent tells you exactly how many 7s to multiply together.

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