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Readme [11.4K]
2 years ago
11

Which expression is equivalent to (r Superscript negative 7 Baseline) Superscript 6? r Superscript 42 StartFraction 1 Over r Sup

erscript 42 Baseline EndFraction Negative 7 r Superscript 6 StartFraction 1 Over r EndFraction.
Mathematics
2 answers:
vodomira [7]2 years ago
8 0

Power rule of exponents says that the power of the power of a exponent is equal to the multiplying both the powers. The expression which is equal to the given expression is,

\dfrac{1}{(r)^{42}}

The option B is the correct option.

Given information-

The given expression in the problem is,

[(r)^{-7}]^5

<h3>Power rule of exponents</h3>

Power rule of exponents says that the power of the power of a exponent is equal to the multiplying both the powers.

Suppose<em> </em><em>x</em> is a number with power <em>a. </em>The power is power of the power of number <em>x. </em>Then by the power rule of the exponents,

(x^a)^b=x^{ab}

Using the power rule of the exponents given expression can be written as,

[(r)^{-7}]^6=(r)^{-7\times 6} &#10;

[(r)^{-7}]^6=(r)^{-42}

<h3>Negative exponents rule</h3>

Negative exponents rule says that when a power of a number is negative, then write the number in the denominator with the same power with positive sign.Thus,

[(r)^{-7}]^6=\dfrac{1}{(r)^{42}}

Hence the expression which is equal to the given expression is,

\dfrac{1}{(r)^{42}}

The option B is the correct option.

Learn more about the power rule of exponents here;

brainly.com/question/819893

Pavel [41]2 years ago
5 0

The answer is B.

On edge 2022

-Victoria Wiseman

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<u>Step-by-step explanation:</u>

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       23 = 4x - 37

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Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.

  • Since N is the midpoint of KL and KL = 95, then NL = 47.5
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Use trig to solve for ∠L (which equals ∠K):

cos ∠L = \frac{adjacent}{hypotenuse}

cos ∠L = \frac{47.5}{68}

      ∠L = cos⁻¹ (\frac{47.5}{68})

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Triangle sum Theorem:

∠K + ∠L + ∠M = 180°    

45.7 + 45.7 + ∠M = 180

       91.4     + ∠M = 180

                      ∠M = 88.6

       

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