Which expression is true?
4³x4⁴=4¹²
5²x5³>5⁵
3²x3⁵<3⁸
5²x5⁴=5⁸
5²x5⁴=5⁸ is true.
Explanation:
- 5² means "5 squared", which is 5 raised to the power of 2, or 5x5=25.
- 5⁴ means "5 to the fourth power", which is 5x5x5x5=625.
- Therefore, 5²x5⁴ means 25x625, which equals 15,625.
- And 5⁸ means "5 to the eighth power", which is 5x5x5x5x5x5x5x5=390,625.
- So the statement 5²x5⁴=5⁸ is true, because 15,625=390,625.
3²x3⁵<3⁸
because
3^7 < 3^8
and
So the statement 5²x5⁴=5⁸ is true, because 15,625=390,625
WHAT ?????
I apologize for the mistake in my previous answer. The correct explanation for 3²x3⁵<3⁸ is:
- 3² means "3 squared", which is 3 raised to the power of 2, or 3x3=9.
- 3⁵ means "3 to the fifth power", which is 3x3x3x3x3=243.
- Therefore, 3²x3⁵ means 9x243, which equals 2187.
- And 3⁸ means "3 to the eighth power", which is 3x3x3x3x3x3x3x3=6561.
- So the statement 3²x3⁵<3⁸ is true, because 2187 is less than 6561.
Again, I apologize for the confusion.
Look, you do not actually have to calculate the numbers to find that 3^7 is less than 3^8
because
3^8 = 3 * 3^7
You are correct. One can use the property of exponentiation that says a^m * a^n = a^(m+n) to simplify 3²x3⁵<3⁸.
- 3²x3⁵ can be rewritten as 3^(2+5) by the property mentioned above, which is 3^7.
- So the inequality can be written as 3^7 < 3⁸, which is true because 3^8 is equal to 3 * 3^7.
To determine which expression is true, we need to evaluate each expression and compare the results.
Let's start with the first expression:
4³ × 4⁴ = 4¹²
To simplify, we need to compute the value of each exponent separately:
4³ = 4 × 4 × 4 = 64
4⁴ = 4 × 4 × 4 × 4 = 256
4¹² = 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 ≈ 16,777,216
Now, let's check if the equation holds true:
64 × 256 = 16,384
Since 16,384 is not equal to 16,777,216, the first expression (4³ × 4⁴ = 4¹²) is not true.
Moving on to the second expression:
5² × 5³ > 5⁵
Again, we need to calculate the value of each exponent:
5² = 5 × 5 = 25
5³ = 5 × 5 × 5 = 125
5⁵ = 5 × 5 × 5 × 5 × 5 = 3,125
Now, let's check if the equation holds true:
25 × 125 = 3,125
Since 3,125 is equal to 3,125, the second expression (5² × 5³ > 5⁵) is true.
Next, let's move on to the third expression:
3² × 3⁵ < 3⁸
Calculating the value of each exponent:
3² = 3 × 3 = 9
3⁵ = 3 × 3 × 3 × 3 × 3 = 243
3⁸ = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 = 6,561
Now, let's check if the equation holds true:
9 × 243 = 2,187
Since 2,187 is less than 6,561, the third expression (3² × 3⁵ < 3⁸) is true.
Lastly, the fourth expression:
5² × 5⁴ = 5⁸
Finding the value of each exponent:
5² = 5 × 5 = 25
5⁴ = 5 × 5 × 5 × 5 = 625
5⁸ = 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 = 3,125,000
Now, let's check if the equation holds true:
25 × 625 = 15,625
Since 15,625 is not equal to 3,125,000, the fourth expression (5² × 5⁴ = 5⁸) is not true.
In conclusion, the second expression (5² × 5³ > 5⁵) and the third expression (3² × 3⁵ < 3⁸) are true.