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2 years ago

Which of the following expressions is equivalent to the one shown below (3/2)^8

Mathematics

1 answer:

vichka [17]2 years ago

8 0

Option B is the right answer

Step-by-step explanation:

Given expression is:

$(\frac{3}{2})^8$

The exponent properties are used to solve these type of questions,

One of the property states that if an exponent is applied to a fraction, it can be applied to the numerator and denominator separately.

so,

for the given expression, the exponent 8 will be applied to 2 and 3 separately

$(\frac{3}{2})^8 = \frac{3^8}{2^8}$

Hence,

Option B is the right answer

Keywords: Exponents, fractions

Learn more about exponents at:

#LearnwithBrainly

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Sanju wants to sell his artwork at a local fair. He has created 10 pieces of artwork and has spent $44 in creating them. He want

Maru [420]

Answer:

30 dollars

Step-by-step explanation:

Sice he has to make a profit of 300 dollars if you divide 100 by to you get 30.If Sanju sells the artwork at 30 dollars he will make 300 dollars

3 0

3 years ago

Read 2 more answers

Simplify completely. (w^15/w^5)^4 <br> HELP PLEASE

Umnica [9.8K]

Answer:

$w^{40}$

Step-by-step explanation:

To simplify recall exponent rules:

1. An exponent is only a short cut for multiplication. It simplifies how we write the expression.

2. When we multiply terms with the same bases, we add exponents.

3. When we divide terms with the same bases, we subtract exponents.

4. When we have a base to the exponent of 0, it is 1.

5. A negative exponent creates a fraction.

6. When we raise an exponent to an exponent, we multiply exponents.

7. When we have exponents with parenthesis, we apply it to everything in the parenthesis.

We will use these rules to simplify.

Use rule #3 to simplify inside the parenthesis first.

$\frac{w^{15}}{w^5} = w^{10}$

Now simplify the exponent of 4 using rule 6.

$(w^{10})^4 = w^{40}$

8 0

2 years ago

Match the identities to their values taking these conditions into consideration sinx=sqrt2 /2 cosy=-1/2 angle x is in the first

BaLLatris [955]

Answer:

$\cos(x+y)$ goes with $-\frac{\sqrt{6}+\sqrt{2}}{4}$

$\sin(x+y)$ goes with $\frac{\sqrt{6}-\sqrt{2}}{4}$

$\tan(x+y)$ goes with $\sqrt{3}-2$

Step-by-step explanation:

$\cos(x+y)$

$\cos(x)\cos(y)-\sin(x)\sin(y)$ by the addition identity for cosine.

We are given:

$\sin(x)=\frac{\sqrt{2}}{2}$ which if we look at the unit circle we should see

$\cos(x)=\frac{\sqrt{2}}{2}$ .

We are also given:

$\cos(y)=\frac{-1}{2}$ which if we look the unit circle we should see

$\sin(y)=\frac{\sqrt{3}}{2}$ .

Apply both of these given to:

$\cos(x+y)$

$\cos(x)\cos(y)-\sin(x)\sin(y)$ by the addition identity for cosine.

$\frac{\sqrt{2}}{2}\frac{-1}{2}-\frac{\sqrt{2}}{2}\frac{\sqrt{3}}{2}$

$\frac{-\sqrt{2}}{4}-\frac{\sqrt{6}}{4}$

$\frac{-\sqrt{2}-\sqrt{6}}{4}$

$-\frac{\sqrt{6}+\sqrt{2}}{4}$

Apply both of the givens to:

$\sin(x+y)$

$\sin(x)\cos(y)+\sin(y)\cos(x)$ by addition identity for sine.

$\frac{\sqrt{2}}{2}\frac{-1}{2}+\frac{\sqrt{3}}{2}\frac{\sqrt{2}}{2}$

$\frac{-\sqrt{2}+\sqrt{6}}{4}$

$\frac{\sqrt{6}-\sqrt{2}}{4}$

Now I'm going to apply what 2 things we got previously to:

$\tan(x+y)$

$\frac{\sin(x+y)}{\cos(x+y)}$ by quotient identity for tangent

$\frac{\sqrt{6}-\sqrt{2}}{-(\sqrt{6}+\sqrt{2})}$

$-\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}+\sqrt{2}}$

Multiply top and bottom by bottom's conjugate.

When you multiply conjugates you just have to multiply first and last.

That is if you have something like (a-b)(a+b) then this is equal to a^2-b^2.

$-\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}+\sqrt{2}} \cdot \frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}-\sqrt{2}}$

$-\frac{6-\sqrt{2}\sqrt{6}-\sqrt{2}\sqrt{6}+2}{6-2}$

$-\frac{8-2\sqrt{12}}{4}$

There is a perfect square in 12, 4.

$-\frac{8-2\sqrt{4}\sqrt{3}}{4}$

$-\frac{8-2(2)\sqrt{3}}{4}$

$-\frac{8-4\sqrt{3}}{4}$

Divide top and bottom by 4 to reduce fraction:

$-\frac{2-\sqrt{3}}{1}$

$-(2-\sqrt{3})$

Distribute:

$\sqrt{3}-2$

6 0

2 years ago

A savings account is started with an initial deposit of $700. The account earns 1.5% interest compounded

marusya05 [52]

Answer:

(a) A = 700×1.015^t

(b) 36.2 years

Step-by-step explanation:

(a) Each year, the account value is multiplied by (1 + 1.5%) = 1.015. Repeated multiplication is signified using an exponent. In t years, when the account has been multiplied by 1.015 t times, the account value will be ...

A = $700×1.015^t

(b) You want to find t when A=$1200. Logarithms are involved.

1200 = 700×1.015^t . . . . use 1200 for A

1200/700 = 1.015^t . . . . . divide by 700

log(12/7) = t×log(1.015) . . . . . take logarithms

log(12/7)/log(1.015) = t ≈ 36.2 . . . . divide by the coefficient of t

It will take about 36.2 years for the account balance to reach $1200.

4 0

3 years ago

James put $1000 in a 2-year CD paying 7% interest, compounded monthly.

ruslelena [56]

To find the future value of this investment the formula is
A=p (1+r/k)^kt
A future value?
P present value 1000
R interest rate 0.07
K compounded monthly 12
T time 2 years
A=1,000×(1+0.07÷12)^(12×2)
A=1,149.81

4 0

3 years ago

Read 2 more answers