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dimaraw [331]
3 years ago
5

Rewrite the expression with a rational exponent as a radical expression.

Mathematics
1 answer:
Nuetrik [128]3 years ago
3 0

Answer:

Rewriting the expression (3^\frac{2}{3})^\frac{1}{6} with a rational exponent as a radical expression we get \mathbf{\sqrt[9]{3} }

Step-by-step explanation:

We need to rewrite the expression (3^\frac{2}{3})^\frac{1}{6} with a rational exponent as a radical expression.

The expression given is:

(3^\frac{2}{3})^\frac{1}{6}

First we will simply the expression using exponent rule (a^m)^n=a^{mn}

(3^\frac{2}{3})^\frac{1}{6}\\=(3^\frac{2}{18})

As we know 2 and 18 are both divisible by 2, we can write

=(3^\frac{1}{9})

Now we know that a^\frac{1}{9}=\sqrt[9]{a}

Using this we get

=\sqrt[9]{3}

So, rewriting the expression (3^\frac{2}{3})^\frac{1}{6} with a rational exponent as a radical expression we get \mathbf{\sqrt[9]{3} }

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This is the easiest way, tho.

60*1.25=75

The correct answer is 75 mph.

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The simplified expression of  $4 x \cdot \frac{1}{x^{-5}} \cdot x^{-3} is 4x^3.

Solution:

Given expression is 4 x \cdot \frac{1}{x^{-5}} \cdot x^{-3}.

To simplify the given expression.

$\Rightarrow4 x \cdot \frac{1}{x^{-5}} \cdot x^{-3}

Using exponent rule: \frac{1}{a^{-m}}=a^m

$\Rightarrow4x \cdot x^{5}.x^{-3}

Using another exponent rule: a^m \cdot a^n=a^{m+n}

$\Rightarrow4x \cdot x^{5-3}

$\Rightarrow4x \cdot x^{2}

Using exponent rule: a^m \cdot a^n=a^{m+n}

$\Rightarrow4x^{1+2}

$\Rightarrow4x^3

Hence the simplified expression of  $4 x \cdot \frac{1}{x^{-5}} \cdot x^{-3} is 4x^3.

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3 years ago
Fourteen more than a number is eighteen.
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Answer: 4

Step-by-step explanation:

18-14=4

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3 years ago
Bobby hopes that he will someday be more than 70 inches tall. he is currently 61 inches tall. how many more inches,
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Bobby should grow an amount greater than 70-61 = 9 inches to become taller than 70 inches. Therefore, the correct answer is that Bobby must grow an amount of x> 9 inches to be taller than 70 inches.
4 0
3 years ago
A rectangular box without a lid is to be made from 48 m2 of cardboard. Find the maximum volume of such a box. SOLUTION We let x,
tatiyna

Answer:

The maximum volume of such box is 32m^3

V = x×y×z = 32 m^3

Step-by-step explanation:

Given;

Total surface area S = 48m^2

Volume of a rectangular box V = length×width×height

V = xyz ......1

Total surface area of a rectangular box without a lid is

S = xy + 2xz + 2yz = 48 .....2

To be able to maximize the volume, we need to reduce the number of variables.

Let assume the rectangular box has a square base,that means; length = width

x = y

Substituting y with x in equation 1 and 2;

V = x^2(z) ....3

x^2 + 4xz = 48 .....4

Making z the subject of formula in equation 4

4xz = 48 - x^2

z = (48 - x^2)/4x .......5

To be able to maximize V, we need to reduce the number of variables to 1, by substituting equation 5 into equation 3

V = x^2 × (48 - x^2)/4x

V = (48x - x^3)/4

differentiating V with respect to x;

V' = (48 - 3x^2)/4

At the maximum point V' = 0

V' = (48 - 3x^2)/4 = 0

Solving for x;

3x^2 = 48

x = √(48/3)

x = √(16)

x = 4

Since x = y

y = 4

From equation 5;

z = (48 - x^2)/4x

z = (48 - 4^2)/4(4)

z = 32/16

z = 2

The maximum volume can be derived by substituting x,y,z into equation 1;

V = xyz = 4×4×2 = 32 m^3

7 0
3 years ago
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