Which expression has twice the value of 2x2x2x2x2?
The Correct Answer and Explanation is:
To find an expression that has twice the value of ( 2 \times 2 \times 2 \times 2 \times 2 ), we first need to calculate the value of this expression.
Step 1: Calculate the Value of ( 2 \times 2 \times 2 \times 2 \times 2 )
This expression can be rewritten using exponents. The expression ( 2 \times 2 \times 2 \times 2 \times 2 ) represents ( 2^5 ), because it is multiplying the number 2 by itself five times.
Calculating ( 2^5 ):
[
2^5 = 32
]
Step 2: Determine Twice the Value
Next, we need to find twice this value:
[
2 \times 32 = 64
]
Step 3: Find the Expression
Now that we know we are looking for an expression that equals ( 64 ), we can express ( 64 ) in various ways.
One straightforward way to express ( 64 ) is to rewrite it as ( 2^6 ), since:
[
2^6 = 64
]
Another way to express ( 64 ) is to think about addition or multiplication. For example:
- ( 8 \times 8 = 64 )
- ( 4 \times 16 = 64 )
- ( 64 \div 1 = 64 )
Conclusion
In conclusion, an expression that has twice the value of ( 2 \times 2 \times 2 \times 2 \times 2 ) is ( 64 ) or equivalently ( 2^6 ). We can derive this by recognizing that the initial expression ( 2^5 ) equals ( 32 ), and multiplying it by 2 gives us ( 64 ). This demonstrates the concept of exponentiation and multiplication, reinforcing the understanding of how numbers can be represented in different forms.