Simplify: w² x w³ x w-². (b) What is 21 1/4% of Le 80,000.00. (c) At what rate will Le 10,000.00 earn an…

Question

Simplify: w² x w³ x w-². (b) What is 21 1/4% of Le 80,000.00. (c) At what rate will Le 10,000.00 earn an interest of Le 400.00 in 5 years?

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

1. (a) Simplify $w^3 \times w \times w^{-2}$

Apply the rule of exponents for multiplication, which states that when multiplying terms with the same base, you add their exponents.
Remember that $w$ is equivalent to $w^1$ .
$w^3 \times w^1 \times w^{-2} = w^{3+1+(-2)}$
Add the exponents.
$w^{3+1-2} = w^{4-2} = w^2$
The simplified expression is $\boxed{w^2}$ .

1. (b) What is $21\frac{1}{2}\%$ of Le 80,000.00?
Convert the mixed percentage to a decimal.
$21\frac{1}{2}\% = 21.5\%$
To use this in calculation, divide by 100.
$21.5\% = \frac{21.5}{100} = 0.215$
Multiply the decimal by the given amount.
$0.215 \times \text{Le } 80,000.00 = \text{Le } 17,200.00$
The amount is $\boxed{\text{Le } 17,200.00}$ .

1. (c) At what rate will Le 10,000.00 earn an interest of Le 400.00 in 5 years?
Identify the given values for simple interest.
The formula for simple interest is $I = PRT$ , where $I$ is interest, $P$ is principal, $R$ is rate, and $T$ is time.
Given:
$I = \text{Le } 400.00$
$P = \text{Le } 10,000.00$
$T = 5 \text{ years}$
We need to find $R$ .
Rearrange the formula to solve for $R$ .
$R = \frac{I}{PT}$
Substitute the given values into the formula.
$R = \frac{400}{10,000 \times 5}$
Perform the multiplication in the denominator and then the division.
$R = \frac{400}{50,000}$ $R = \frac{4}{500}$ $R = \frac{1}{125}$ $R = 0.008$
Convert the decimal rate to a percentage by multiplying by 100.
$R = 0.008 \times 100\% = 0.8\%$
The rate is $\boxed{0.8\% \text{ per annum}}$ .

Simplify: w² x w³ x w-². (b) What is 21 1/4% of Le 80,000.00. (c) At what rate will Le 10,000.00 earn an interest of Le 400.00 in 5 years?