Powers: Identify the greater value

Question 1

Which is larger?

$0^{100}\text{ }_{——}100^0$

Question 2

Which is larger?

$5^2\text{ }_{——}2^5$

Question 3

Which is larger?

$6^1\text{ }_{——}1^6$

Question 4

Which of the expressions has the highest value?

$6^{25},7^{15},9^{13},2^{45}$

Question 5

Which of the expressions below has the highest value?

$7^4,8^3,10^2,11^{\frac{1}{2}}$

Examples with solutions for Powers: Identify the greater value

Exercise #1

Which is larger?

$0^{100}\text{ }_{——}100^0$

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Evaluate $0^{100}$ .
Step 2: Evaluate $100^0$ .
Step 3: Compare the values obtained in Step 1 and Step 2.

Now, let's work through each step:

Step 1: Evaluate $0^{100}$ .
Any non-negative integer power of 0 evaluates to 0. Therefore, $0^{100} = 0$ .

Step 2: Evaluate $100^0$ .
By the zero exponent rule for non-zero bases, $100^0 = 1$ .

Step 3: Compare the values obtained: $0$ and $1$ .
Clearly, $0 < 1$ .

Therefore, $0^{100}$ is less than $100^0$ .

The correct choice is: $<$

Answer

$<$

Exercise #2

Which is larger?

$5^2\text{ }_{——}2^5$

Video Solution

Answer

$<$

Exercise #3

Which is larger?

$6^1\text{ }_{——}1^6$

Video Solution

Answer

$>$

Exercise #4

Which of the expressions has the highest value?

$6^{25},7^{15},9^{13},2^{45}$

Video Solution

Answer

$6^5$

Exercise #5

Which of the expressions below has the highest value?

$7^4,8^3,10^2,11^{\frac{1}{2}}$

Video Solution

Answer

$7^4$

Question 1

Which expression is of greater value:

Question 2

Which is larger?

$7^2\text{ }_{——}7^3$

Question 3

Which is larger?

$2^4\text{ }_{——}4^2$

Question 4

Which is larger?

$(\frac{1}{2})^5\text{ }_{——}(0.5)^5$

Question 5

Which of the expressions below has the highest value?

Exercise #6

Which expression is of greater value:

Video Solution

Answer

$5^5$

Exercise #7

Which is larger?

$7^2\text{ }_{——}7^3$

Video Solution

Answer

$<$

Exercise #8

Which is larger?

$2^4\text{ }_{——}4^2$

Video Solution

Answer

$=$

Exercise #9

Which is larger?

$(\frac{1}{2})^5\text{ }_{——}(0.5)^5$

Video Solution

Answer

$=$

Exercise #10

Which of the expressions below has the highest value?

Video Solution

Answer

$12^4$

Question 1

Which is larger?

$16^8\text{ }_{——}16^{(2+6)}$

Question 2

Which is larger?

$(\frac{3}{10})^7\text{ }_{——}(0.3)^8$

Exercise #11

Which is larger?

$16^8\text{ }_{——}16^{(2+6)}$

Video Solution

Answer

$=$

Exercise #12

Which is larger?

$(\frac{3}{10})^7\text{ }_{——}(0.3)^8$

Video Solution

Answer

$<$