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miv72 [106K]
3 years ago
9

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

Mathematics
2 answers:
agasfer [191]3 years ago
7 0

Answer:

The correct answer is B. \sqrt[9]{3}

Step-by-step explanation:

The root of a number can be expressed as the number raised to the power whose exponent is a fractional number. The exponent number will be the inverse of the root index.

In this case, three to the two thirds power all raised to the one sixth power is expressed as:

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

Power of a Power Property: This property states that the power of a power can be found by multiplying the exponents.

So, we multiply the exponents:

\frac{2}{3} \times \frac{1}{6}= \frac{1}{9}

The expression would be:

3^{\frac{1}{9} }

which as a radical expression is:

\sqrt[9]{3}

The four options are expressed as:

a) \sqrt[6]{3}

b) \sqrt[9]{3}

c) \sqrt[18]{3}

d) \sqrt[6]{3^3}

The correct answer is B.

STatiana [176]3 years ago
5 0

The answer should be B.

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15

Step-by-step explanation:

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Lenny and Lisa have obtained a 30-year, fixed rate mortgage for $675,250 with a 7.25% interest rate. They purchased 3 points and
Vikentia [17]

Answer:

119 months

Step-by-step explanation:

In this question, we are asked to calculate the amount of time it would take for a break-even point on a mortgage, if there is a factoring in the cost of points.

We proceed to answer the;

Mathematically,

The Break Even Point = Amount Paid for purchasing Discount Points divided by Monthly savings in the interest payments

We lost out the important values given in the question as follows:

Amount of Mortgage - $675,250

Tenure - 30 Years

The Rate of interest without points = 7.25%

The number of points = 3 points

The rate of interest with the 3 points = 6.875%

The amount to be paid for purchasing the discount point is now calculated below;

Since 1 discount point = 1% of mortgage value;

Therefore, 3 discount points = 3% of mortgage value

The amount paid is thus = 3% of $675,250 = $20,257.5

To calculate Monthly payment without points, we use the mathematical formula;

M = P[r(1+r)^n/((1+r)^n)-1)]

Where M

Is monthly payment, r is the interest rate, n is the number of months.

According to the question M = 675,250, r = 7.25% = 7.25/100 = 0.0725 , n= 30 * 12 months = 360 months

M = 675,250[0.0725(0.0725+1)^30/(1+0.0725)^360)-1) = $4606.40

To get the monthly payment with points, we simply use the formula again but this time interest rates will be 6.875% = 0.06875 I.e r = 0.06875

Inputting the terms in the formula will yield a value of $4435.91. This means monthly payment with discount will be $4435.91

Savings in monthly payments after purchasing the discount points = $4,606.40 - $4,435.91 = $170.48

Break Even = Purchase cost of Discount Points / Monthly savings

= $20,257.5 / $170.48

= 119 Months

Hence, the number of months it will take Lisa and Lenny to break-even point on their mortgage will be 119 months

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3 years ago
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Answer:

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Step-by-step explanation:

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Simplify the following expression.
HACTEHA [7]
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