All categories

3 years ago

Which rules of exponents will be used to evaluate the expression. Check all that apply

Mathematics

2 answers:

julia-pushkina [17]3 years ago

6 0

Hello!

The answer are:

- Product of powers.

- Power of a power.

- Negative exponents.

Let's solve it!

It's a math rule that we must solve first what's into a brake or parenthesis, so,

First: Product of powers $[(7)^{5}*(7)^{3}]$

According to the exponent's law, we have a product of powers case, so, we need to sum the exponents and keep the base

Exponents: 5 and 3

Base: 7

Applying it we have:

$(7)^{5+3}$

$(7)^{8}$

Then,

We have a power of a power case, which involves multiplying the exponents:

$[(7)^{5}*(7)^{3}]^{-4}$

Exponents: 3 and -4

Then,

$(7)^{8*-4}$

Finally, we can apply the negative exponents, the negative exponent's rules state that negative exponents are the reciprocal of the positive exponents,

So, we will have that:

$(7)^{-32}=\frac{1}{7^{32} }$

Have a nice day!

andriy [413]3 years ago

3 0

Answer:

Three rules are used

1) Product of powers

2) Power of a power

3) Negative exponents

Step-by-step explanation:

The given expression is [(7)⁵(7)³]⁻⁴

<u>To find the value of [(7)⁵(7)³]⁻⁴ </u>

[(7)⁵(7)³]⁻⁴ = [(7)⁵⁺³]⁻⁴ = [(7)⁸]⁻⁴(using product of powers rule)

[(7)⁵⁺³]⁻⁴ = [(7)⁸ˣ⁻⁴] = 7⁻³² [using powers of power rule)

7⁻³² = 1/7³² (using negative exponent rule)

Using three rules we can solve [(7)⁵(7)³]⁻⁴

Therefore the correct answers are

1) Product of powers

2) Power of a power

3) Negative exponents

You might be interested in

Each set of numbers below represents the lengths of three line segments. Which set represent line segments that could be connect

LenKa [72]

Answer:

B is the triangle

A and E can be thought of as triangles as well with angles 0°, 0° and 180°, but it will be just a line with 3 points. So it depends whether this is a question with multiple answers or not.

Step-by-step explanation:

Thinking Process:

We need to find a formula for a triangle that uses all the sides

Cosine rule uses all sides:

$c^2 = a^2 + b^2 -2ab(cosA)$

we can rearrage this formula and make the angle $A$ the subject:

$A = cos^{-1}(\frac{a^2+b^2-c^2}{2ab})$

now you can just put the values from each option in the question into this formula and see if it gives an answer or not.

put a = 1, b = 2, c = 3 (keep in mind that you can take 'a' 'b' and 'c' as 3,2 and 1 or any other arrangement within the option A(1,2,3). All we are doing here is checking whether the answer exists or not)

$A = cos^{-1}(\frac{1^2+2^2-3^2}{2(1)(2)})$

$A = 180$ , now graphically it seems that this is just a line with 3 points, or technically you can think of as the sides of the triangle are overlapping each other, and the angle between the sides is 0 0 and 180. It depends on whether the question is asking you to be technical or not. Since the question already stated there are 3 line segments, so we can think of it as a triangle.

$A = cos^{-1}(\frac{3^2+4^2-5^2}{2(3)(4)})$

$A = 90$ , this is a triangle (specifically, this is a right angled triangle)

$A = cos^{-1}(\frac{1^2+10^2-100^2}{2(1)(10)})$

from the calculator you'll see a 'math error', this shows that there is no answer, because $cos^{-1}$ can only accept values within -1 and 1 inclusive. Hence no such triangle exists with lengths (1,10,100).

Similarly you can try the formula with all other options, and find whose answers exists or not.

Finally, to complete the answer, let's

Try E.(1,3,4)

$A = cos^{-1}(\frac{1^2+3^2-4^2}{2(1)(3)})$

$A = 180$ , hence this is also one of those "3 points on a straight line triangles" similar to A(1,2,3)

so the answer is either A,B and E OR just B

Hope this helps :)

5 0

3 years ago

I’m having a very hard time with this. please help.

boyakko [2]

You multiply 5 x 3 Bc you multiplied the left side by 3. Hope this helps

8 0

2 years ago

A horizontal line passes through (0,7). write the point-slope of its equation.

Nuetrik [128]

Answer:y-7=m(x-0)

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

And multiply

Lilit [14]

Answer:

91 grams

Step-by-step explanation:

To get a percentage you go the number which you want the percentage of divided by the full number then multiply all that by 100. For example, (10 / 100) x 100 = 10, so 10 is 10% of 100.

Now lets call the answer x:

(x / 130g) x 100 = 30%

Now you need to get x on its own, so you need to rearrange it:

x = (30 x 130) / 100

When you change the sides, you change the signs.

With this equation we can work out what 30% of 130 is. So,

(30 x 130) / 100 = 39g

So, 39g is 30%. To find out how much sugar is in the diet juice you need to subtract this from the regular cranberry juice sugar:

130 - 39 = 91g

So there is 91 grams of sugar in a serving or diet juice.

7 0

3 years ago

*ill mark brainliest*

Sphinxa [80]

It would be 143 because if you were to multiply 100*11 = 1100 so doing the same for 13*11 would equal 143

4 0

3 years ago