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3 years ago

How do you simplify (2xy2)3

1 answer:

4 0

$(2xy^{2})^{3} = (2xy^{2})(2xy^{2})(2xy^{2})$
Now, we can just multiply it and obtain the result
$(2xy^{2})(2xy^{2})(2xy^{2})=(4x^{2}y^{4})(2xy^{2})=8x^{3}y^{6}$

I used law presented on this example
$2^{3}*2=2^{3}*2^{1}=2^{3+1}=2^{4}$

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Question 1) When multiplying powers with the same base, keep the base and _______________ the exponents.

nika2105 [10]

The rules are

$x^a\cdot x^b = x^{a+b}$

$\dfrac{x^a}{x^b} = x^{a-b}$

Let me show you why with a couple of examples: suppose we want to multiply

$4^3\cdot 4^2$

Since powers are just repeated multiplications, we have

$4^3\cdot 4^2 = \underbrace{4\cdot 4\cdot 4}_{4^3}\cdot\underbrace{4\cdot 4}_{4^2}=4^5 = 4^{3+2}$

Similarly, we have

$\dfrac{4^3}{4^2} = \dfrac{4\cdot 4 \cdot 4}{4\cdot 4} = 4 = 4^1 = 4^{3-2}$

8 0

3 years ago

Plz help I’m stuck and I can’t answer

Margaret [11]

Answer: the first one is 14 and the second one is 5

Step-by-step explanation:

7 0

3 years ago

Hye Sun has a modern coffee table whose top is a triangle with the following side legngths: 8 feet , 3 feet, and 5 feet. Is Hye

ale4655 [162]

8 feet is the longest side so it would be the hypotenuse. Use the Pythagorean formula to check.
a^2 + b^2 = c^2
3^2+5^2 = 8^2
9 + 25 = 64
34 = 64
This is obviously not true si it is not a right triangle.

3 0

3 years ago

F(x)= 6x-7 g(x)=6x+7, f(g(x))= and g(f(x))=

horrorfan [7]

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6 0

2 years ago

Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your

Law Incorporation [45]

Answer:

According to the rule of 72, the doubling time for this interest rate is 8 years.

The exact doubling time of this amount is 8.04 years.

Step-by-step explanation:

Sometimes, the compound interest formula is quite complex to be solved, so the result can be estimated by the rule of 72.

By the rule of 72, we have that the doubling time D is given by:

$D = \frac{72}{Interest Rate}$

The interest rate is in %.

In our exercise, the interest rate is 9%. So, by the rule of 72:

$D = \frac{72}{9} = 8$ .

According to the rule of 72, the doubling time for this interest rate is 8 years.

Exact answer:

The exact answer is going to be found using the compound interest formula.

$A = P(1 + \frac{r}{n})^{nt}$

In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

is double the initial amount, double the principal.

$A = 2P$