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3 years ago

Use the properties of exponents to simplify the expression: y^(y3)2

Mathematics

1 answer:

iren [92.7K]3 years ago

8 0

because y^3 is raised to the power of two, we will have to multiply the exponents rather than adding them.

By distributing the power of 2, we will get y^2(6).

Because now the exponents are being multiplied, we can just add them to get y^8. The other y has a power of 1, so we'll just add the power of that y as well to get y^9.

summary:

multiply exponents if they are being raised to a power.

add exponents if they are being multiplied, and only add them if they have the same base (in this case, both the bases of the exponents are y, so we can add them)

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Apply the distributive property to factor out the greatest common factor.<br> 56<br> +<br> 32<br> =

valentina_108 [34]

Answer:

8 * (7 + 4)

See process below

Step-by-step explanation:

We start by writing each number in PRIME factor form:

56 = 2 * 2 * 2 * 7

32 = 2 * 2 * 2 * 2 * 2

Notice that the factors that are common to BOTH numbers are 2 * 2 * 2 (the product of three factors of 2).Therefore we see that the greatest common factor for the given numbers is : 2 * 2 * 2 = 8

Using this, we can write the two numbers as the product of this common factor (8) times the factors that are left on each:

56 = 8 * 7

32 = 8 * 2 * 2 = 8 * 4

We can then use distributive property to "extract" that common factor (8) from the given addition as shown below:

56 + 32

8 * 7 + 8 * 4

8 * (7 + 4)

8 * (11)

4 0

3 years ago

What is the solution for the equation StartFraction 5 Over 3 b cubed minus 2 b squared minus 5 EndFraction = StartFraction 2 Ove

wolverine [178]

Answer:

The solutions are:

$b=0,\:b=4$

Step-by-step explanation:

Considering the expression

$\frac{5}{3b^3-2b^2-5}=\frac{2}{b^3-2}$

Solving the expression

$\frac{5}{3b^3-2b^2-5}=\frac{2}{b^3-2}$

$\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c$

$5\left(b^3-2\right)=\left(3b^3-2b^2-5\right)\cdot \:2$

$5b^3-10=6b^3-4b^2-10$

$\mathrm{Switch\:sides}$

$6b^3-4b^2-10=5b^3-10$

$6b^3-4b^2-10+10=5b^3-10+10$

$6b^3-4b^2=5b^3$

$\mathrm{Subtract\:}5b^3\mathrm{\:from\:both\:sides}$

$6b^3-4b^2-5b^3=5b^3-5b^3$

$b^3-4b^2=0$

$Using\:the\:Zero\:Factor\:Principle:$ $if\:\mathrm ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)$

So,

$b=0,b-4=0$

$b=0,b=4$

Therefore, the solutions are:

$b=0,\:b=4$

4 0

3 years ago

Read 2 more answers

Could someone do all the problems and/or check my work?

MArishka [77]

11. You’ve done it correctly

12. Let x^2=y
y^2+13y+40=0
(y+8)(y+5)=0
y=8, 5
Since y=x^2
x^2=8 x^2=5
x=+/-√5 x= +/-2√2

13. x^4-x^2-x^2-8=0
x^4-2x^2-8=0
let x^2=y
Y^2-2y-8=0
(y-4)(y+2)=0
y=4, -2
Since y=x^2
X^2=4 X^2=-2
X= +/- 2 This wouldn’t be a real solution

14. It’s pretty much the same process, just substitute y in for x^2. If you’re confused feel free to ask and I can do it, or you can put it through Photomath

15. You’re on the right track so I’m just going to continue from where you left off
x^2(4x+5)-4(x+5)=0
(x^2-4)(4x+5)=0
x= +/- 2 4x=5
x=5/4 or 1 1/4

Hope this helped :)

8 0

3 years ago

Read 2 more answers

A 400-g sample of a radioactive substance is placed in a chamber to be tested. After 3 h,

muminat

Answer:

You left out the quantity of grams remaining.

Step-by-step explanation:

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3 years ago

Chef Johnson used 4 1/2 cups of flour of flour to make 4 fruitcakes.How many cups of flour are needed for 1 fruitcake?

andrezito [222]

Answer:

1 1/8

Step-by-step explanation:

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3 years ago