Calculate 16³: Converting Power to Integer Value

Exponent Calculation with Cube Powers

Write the following as an integer:

163= 16^3=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's solve this problem together.
00:07 We'll use something called the power formula.
00:11 Whenever you see X, to the power of N.
00:14 It means X, times itself, N times.
00:25 Now, let's use this formula in our exercise.
00:31 We will break down the power, into simple multiplications.
00:41 Next, let's calculate these multiplications.
00:50 And there you have it! That's the solution to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Write the following as an integer:

163= 16^3=

2

Step-by-step solution

To solve this problem, we will compute 163 16^3 by performing the following steps:

  • First, calculate the square of 16: 16×16=256 16 \times 16 = 256 .
  • Next, use the result to find 163 16^3 : 256×16=4096 256 \times 16 = 4096 .

Therefore, the value of 163 16^3 is 4096 4096 .

3

Final Answer

4096

Key Points to Remember

Essential concepts to master this topic
  • Cube Rule: a3=a×a×a a^3 = a \times a \times a means multiply the base three times
  • Technique: Break down 163 16^3 as 162×16=256×16 16^2 \times 16 = 256 \times 16
  • Check: Verify by counting digits: 163=4096 16^3 = 4096 has 4 digits ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying the base by the exponent
    Don't calculate 163 16^3 as 16×3=48 16 \times 3 = 48 ! This confuses exponents with multiplication and gives completely wrong answers. Always multiply the base by itself the number of times shown in the exponent.

Practice Quiz

Test your knowledge with interactive questions

\( 11^2= \)

FAQ

Everything you need to know about this question

Is there a shortcut to calculate 163 16^3 without doing all the multiplication?

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Yes! Since 16 = 2⁴, you can use the power rule: 163=(24)3=212=4096 16^3 = (2^4)^3 = 2^{12} = 4096 . But the step-by-step method is more reliable for beginners.

Why do we calculate 162 16^2 first instead of doing 16×16×16 16 \times 16 \times 16 all at once?

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Breaking it down makes it easier and less error-prone! Calculate 162=256 16^2 = 256 first, then multiply by 16 once more. This reduces the chance of arithmetic mistakes.

How can I remember what 163 16^3 equals?

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Practice with patterns! Remember that 162=256 16^2 = 256 and 163=4096 16^3 = 4096 . Notice that 4096 is exactly 16 times larger than 256.

What if I get a different answer when I check my work?

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Double-check your multiplication! The most common errors happen in the arithmetic steps. Write out each step clearly: 16×16=256 16 \times 16 = 256 , then 256×16=4096 256 \times 16 = 4096 .

Are there other ways to think about 163 16^3 ?

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Yes! You can think of it as the volume of a cube with side length 16 units. Each side is 16, so the volume is 16×16×16=4096 16 \times 16 \times 16 = 4096 cubic units.

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