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Simplify: w² x w x w⁻². (b) What is 21½ % of Le 80,000.00. (c) At what rate will Le 10,000.00 earn an interest of Le 400.00 in 5 years?

Mathematics

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3 parts
a

w

b

Le 17,200.00\text{Le } 17,200.00

c

0.8%0.8\%

Step-by-step solution

8 steps

here are the solutions to the questions:

1.

Part a· 2 steps

Simplify: w2×w×w−2w^2 \times w \times w^{-2}.

  1. Apply the rule of exponents for multiplication, am×an=am+na^m \times a^n = a^{m+n}.

    w2×w1×w−2=w2+1+(−2)w^2 \times w^1 \times w^{-2} = w^{2+1+(-2)}

  2. Add the exponents.

    w2+1−2=w1=ww^{2+1-2} = w^1 = w

    The simplified expression is w\boxed{w}.

Part b

Le 17,200.00\text{Le } 17,200.00

What is 2112%21 \frac{1}{2}\% of Le 80,000.00.

  1. Convert the percentage to a decimal.

    2112%=21.5%=21.5100=0.21521 \frac{1}{2}\% = 21.5\% = \frac{21.5}{100} = 0.215

  2. Multiply the decimal by the amount.

    0.215×Le 80,000.00=Le 17,200.000.215 \times \text{Le } 80,000.00 = \text{Le } 17,200.00

    2112%21 \frac{1}{2}\% of Le 80,000.00 is Le 17,200.00\boxed{\text{Le } 17,200.00}.

Part c

0.8%0.8\%

At what rate will Le 10,000.00 earn an interest of Le 400.00 in 5 years?

  1. Identify the given values

    Principal (PP) = Le 10,000.00, Interest (II) = Le 400.00, Time (TT) = 5 years. Use the simple interest formula I=PRTI = PRT.

    400=10000×R×5400 = 10000 \times R \times 5

  2. Simplify the right side of the equation.

    400=50000×R400 = 50000 \times R

  3. Solve for the rate (RR).

    R=40050000R = \frac{400}{50000} R=4500=1125=0.008R = \frac{4}{500} = \frac{1}{125} = 0.008

  4. Convert the decimal rate to a percentage.

    R=0.008×100%=0.8%R = 0.008 \times 100\% = 0.8\%

    The rate is 0.8%\boxed{0.8\%}.

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