Which of the following expressions is true?
2⁴x2⁴>2⁷
3²x3⁶=3⁷
4³x4⁵<4⁸
5²x5³=5⁶
4³x4⁵<4⁸
2^8 is > 2^7 This is the only true one
3^8 is not = 3^7
4^8 is not , < 4^8
5^5 is not 5^6
I apologize for my previous response. It contained errors. The correct answer is:
2⁴x2⁴>2⁷
This can be simplified to:
2⁸ > 2⁷
Which is true, since 2⁸ (256) is greater than 2⁷ (128).
The other options are false:
3²x3⁶=3⁷ (3² = 9, 3⁶ = 729, 3⁷ = 2187, so 9 x 729 does not equal 2187)
4³x4⁵<4⁸ (4³ = 64, 4⁵ = 1024, 4⁸ = 65536, so 64 x 1024 is less than 65536)
5²x5³=5⁶ (5² = 25, 5³ = 125, 5⁶ = 15625, so 25 x 125 does not equal 15625)
To determine which of the following expressions is true, we need to simplify each expression and then compare the results.
Let's start with the first expression:
2⁴ x 2⁴ = 16 x 16 = 256
2⁷ = 128
Since 256 is greater than 128, the expression 2⁴ x 2⁴ > 2⁷ is true.
Now let's move onto the second expression:
3² x 3⁶ = 9 x 729 = 6561
3⁷ = 2187
Since 6561 is greater than 2187, the expression 3² x 3⁶ > 3⁷ is true.
Next, let's evaluate the third expression:
4³ x 4⁵ = 64 x 1024 = 65536
4⁸ = 65536
Since both sides are equal, the expression 4³ x 4⁵ = 4⁸ is true.
Lastly, let's compute the fourth expression:
5² x 5³ = 25 x 125 = 3125
5⁶ = 15625
Since 3125 is less than 15625, the expression 5² x 5³ < 5⁶ is false.
So, the true statements are:
- 2⁴ x 2⁴ > 2⁷
- 3² x 3⁶ > 3⁷
- 4³ x 4⁵ = 4⁸
The false statement is:
- 5² x 5³ < 5⁶