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Alja [10]
3 years ago
12

Rational Exponent

Mathematics
2 answers:
liq [111]3 years ago
4 0

Answer:

Sample Response:

Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Step-by-step explanation:


lara [203]3 years ago
3 0
The concept of radicals and radical exponents is tricky at first, but makes sense when we look into the logic behind it. 

When we write a radical in exponential form, like writing √x as x^(1/2), we are simply putting the power of the radical in the denominator (bottom number) of the exponent, and the numerator is the power we raise the exponent to, or the power that would be inside the radical. 
In our example, √x is really ²√(x¹), or the square root of x to the first power. For this reason, we write it as x^(1/2).

Let's say we wanted to write the cubed root of x squared, in exponential form. 
In radical form, it would look like this:
³√(x²) . This means we square x, and then take the cubed root.
In exponential form, remember that we take the power of the radical (3), and make that the denominator of the exponent, and keep the numerator as the power that x is raised to (2). 
Therefore, it would be x^(2/3), or x to the 2 thirds power. 

Just like when multiplying by a fraction, you multiply by the numerator and divide by the denominator, in exponential form, you raise your base number to the power of the numerator, and take the root of the denominator. 
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Step-by-step explanation:

a = -52 - b / 4

b = -52 - 4a

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5 0
3 years ago
HELP ASAP PLEASE!!!!!
nataly862011 [7]

The answer is A. a=(-1) b=(7)

5 0
3 years ago
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The radius of a small ball is around 4.89796 cm. the radius of a basketball is about 2.45 times larger. what is the ratio of the
expeople1 [14]
Formula for surface area of a sphere of radius r is A = 4pi*r^2.

The same formula, for the case where the radius is 2.45 times greater, comes out to A = 4pi*[2.45r]^2.

Just find the ratio of

4pi*r^2 to 4pi*[2.45r]^2.  It is 1/6.


6 0
3 years ago
A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.What is the
oksian1 [2.3K]

Area of a triangle is given by half the product of two of the sides and the sine of the included angle.

Thus, the area of the triangle is 0.5 x 27.6 x 30 x sin 23^o = 161.76 cm^2

7 0
3 years ago
Akira receives a prize at a science fair for having the most informative project. Her trophy is in the shape of a square pyramid
PolarNik [594]

Akira needs 45 square inches of  gold foil to cover the chair free including the bottom​

Step-by-step explanation:

Total surface  =  surface area of the base square + area of 4 triangles

Step 1: The surface area of the base square

surface area of the base = surface area of the square =  

where s is the side length

The the surface area of the base  = = 9 square inches

Step 2: The surface area of the side triangles

The area of the triangle =

On substituting the values,

The area of the triangle =

The area of the triangle =

The area of the triangle = 9 square inches

Now the area of 4 triangles  =  4 x 9  = 36 square inches

Thus the total surface area  =  9 + 36 = 45 square inches

3 0
3 years ago
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