Find the Mean 10^2 , (5^2-11)÷( square root of 49)-3^3

$10^{2}$ , $(5^{2} - 11) \div \sqrt{49} - 3^{3}$

Step 1

Raise $10$ to the power of $2$ .

$100, (5^{2} - 11) \div \sqrt{49} - 3^{3}$

Step 2

Simplify each term.

Rewrite the division as a fraction.

$100, \frac{5^{2} - 11}{\sqrt{49}} - 3^{3}$

Simplify the numerator.

Raise $5$ to the power of $2$ .

$100, \frac{25 - 11}{\sqrt{49}} - 3^{3}$

Subtract $11$ from $25$ .

$100, \frac{14}{\sqrt{49}} - 3^{3}$

Simplify the denominator.

Rewrite $49$ as $7^{2}$ .

$100, \frac{14}{\sqrt{7^{2}}} - 3^{3}$

Pull terms out from under the radical, assuming positive real numbers.

$100, \frac{14}{7} - 3^{3}$

Divide $14$ by $7$ .

$100, 2 - 3^{3}$

Raise $3$ to the power of $3$ .

$100, 2 - 1 \cdot 27$

Multiply $- 1$ by $27$ .

$100, 2 - 27$

Step 3

Subtract $27$ from $2$ .

$100, - 25$

Step 4

The mean of a set of numbers is the sum divided by the number of terms.

$\frac{100 - 25}{2}$

Step 5

Subtract $25$ from $100$ .

$\frac{75}{2}$

Step 6

Divide.

$37.5$