Evaluate all numerical expressions with exponents

Mathematics

1 answer:

Eduardwww [97]2 years ago

7 0

Y to the power of 2 over 2x to the power of 3

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How to right a radical in exponential form

Law Incorporation [45]

Answer:

$\sqrt[n]{x}=x^{\frac{1}{n}}$

Step-by-step explanation:

The index of a radical is the denominator of a fractional exponent, and vice versa. If you think about the rules of exponents, you know this must be so.

For example, consider the cube root:

$\sqrt[3]{x}\cdot \sqrt[3]{x}\cdot \sqrt[3]{x}=(\sqrt[3]{x})^3=x\\\\(x^{\frac{1}{3}})^3=x^{\frac{3}{3}}=x^1=x$

That is ...

$\sqrt[3]{x}=x^{\frac{1}{3}} \quad\text{radical index = fraction denominator}$

3 0

3 years ago

A line intersects the points(-22,-14) and (-18,-12). What is the slope-intercept equation for this line?

zaharov [31]

Hello there,

Well we are going to start off with the equation to find the slope based on the given points:

$\frac{y_{2} - y_{1} }{x_{2} -x_{1} }$

Now using the two given points we are going to plug in and solve:

$\frac{(-12)-(-14)}{(-18)-(-22)}$ = $\frac{2}{4}$ = $\frac{1}{2}$

From this you know that $\frac{1}{2}$ is the slope of the equation. However, to find the y-intercept we are going to use y = mx+ b and plug in one of the points to solve:

(-14) = $\frac{1}{2}$ (-22) + b

(-14) = (-11) + b

-3 = b

That means that the y-intercept is at (0, -3). Lastly, we are just going to plug all this into the slope-intercept form:

y = $\frac{1}{2}$ - 3

Hope I helped,

Amna

6 0

3 years ago

What is the average rate of change of the function f(x)=2x+4 over the interval -4 ≤ x ≤ 1? Table

Tom [10]

Answer: