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leva [86]
1 year ago
15

Write each expression in simplest form. (x²/x⁻¹¹)¹/₃

Mathematics
1 answer:
aleksklad [387]1 year ago
8 0

The result of simplifying the expression (x²/x⁻¹¹)¹/₃ using the exponent rules is \sqrt[3]{}(x¹³)

To solve this exercise we have to resolve algebraic operations following the exponent rules.

(x²/x⁻¹¹)¹/₃

Using the quotient rule that indicates that: the exponent result will be the subtraction of these exponents, we have:

(x⁽²⁻⁽⁻¹¹⁾)¹/₃

(x⁽²⁺¹¹⁾)¹/₃

(x¹³)¹/₃

Using the power of a power rule that indicates that: the exponent result will be the multiplication of these powers, we have:

x⁽¹³*¹/₃⁾

x⁽¹³/₃⁾

As we have a fractional exponent, you must convert the exponent to root:

\sqrt[3]{}(x¹³)

<h3>What is an exponent?</h3>

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

Learn more about exponent at: brainly.com/question/847241

#SPJ4

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Answer:

Step-by-step explanation:

Note: I will leave the answers as fraction and in terms of pi unless the question states rounding conditions to ensure maximum precision.

From the question, we can tell it is a inversed-cone (upside down)

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We will now find the volume of the cone.

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b) After 1 hour, we know that the new radius = 7.75cm - 0.35cm = 7.4cm

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Volume of cone being melted = New Volume - Original volume

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c) Lets take the bucket as a round cylinder.

Given radius of bucket, r = 12.5cm (Half of Diameter) and h , height = 30cm.

Volume of cylinder = \pi r^{2} h\\=\pi (12.5)^{2} (30)\\=\frac{9375\pi }{2} cm^{3}

To overflow the bucket, the volume of ice melted must be more than the bucket volume.

Volume of ice melted after 5 hours = 5(\frac{35697\pi }{40} )\\=\frac{35697\pi }{8} cm^{3}

See, from here of course you are unable to tell whether the bucket will overflow as all are in fractions, but fret not, we can just find the difference.

Volume of bucket - Volume of ice melted after 5 hours

= \frac{9375\pi }{2} -\frac{35697\pi }{8 } \\=\frac{1803\pi }{8}cm^{3}

from we can see the bucket can still hold more melted ice even after 5 hours therefore it will not overflow.

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