Which is the value of this expression when a = 5 and k = negative 2?

Mathematics

1 answer:

LuckyWell [14K]2 years ago

6 0

Answer:

Step-by-step explanation:

hello :

this expression equivalent to : (3/a)^5

because ;3²a^(-2)/3a^(-1)= (3²/3)×(a^(-2)/a^(-1)) = 3a^(-2+1) = 3a^(-1) = 3/a

now : a=5 and k= -2 so : (3/5)^(-2) = (5/3)² =25/9

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Work Shown:

$112 \text{ in}^2 = 112 \text{ in}^2 \times \frac{2.54 \text{ cm}}{1 \text{ in}} \times \frac{2.54 \text{ cm}}{1 \text{ in}}\\\\112 \text{ in}^2 = (112 \times 2.54 \times 2.54) \text{ cm}^2\\\\112 \text{ in}^2 = 112 \times (2.54)^2 \text{ cm}^2\\\\112 \text{ in}^2 = 722.5792 \text{ cm}^2\\\\$

Notes:

1 inch = 2.54 cm exactly
The conversion factor $\frac{2.54 \text{ cm}}{1 \text{ in}}$ is used to convert from inches to cm. The inches unit in the denominator cancels with one of the inches unit from the original 112 square inches figure.
We use two identical copies of the same conversion factor to convert from square inches to square centimeters. This is the "multple conversion" your teacher is referring to.
Think of "square inches", aka $\text{in}^2$ , as "inches times inches". Or think of a 1 inch by 1 inch square that has an area of 1 square inch. The same applies for the square centimeter unit as well.