Write the equation in standard form.

NEED HELP ASAP 70 POINTS

Nataliya [291]

Answer:

1) Option A) is correct

The given rational exponent expression is not simplified correctly as a radical expression is

$x^{\frac{7}{4}}=\sqrt[7]{x^4}$

2)Option A) is correct

That is $(729x^3y^{-18})^{\frac{1}{6}}=\frac{3\sqrt{x}}{y^3}$

Step-by-step explanation:

1) Given that $x^{\frac{7}{4}}=(\sqrt{x^7})^\frac{1}{4}$

$x^{\frac{7}{4}}=\sqrt[4]{x^7}$ is the correct answer but in the given problem they gave the RHS as wrong.

Therefore the given rational exponent expression is not simplified correctly as a radical expression is

$x^{\frac{7}{4}}=\sqrt[7]{x^4}$

2)Given that the rational exponent expression is $(729x^3y^{-18})^{\frac{1}{6}}$

To find it as a radical expression:

$(729x^3y^{-18})^{\frac{1}{6}}=(729)^{\frac{1}{6}}(x^3)^{\frac{1}{6}}((y^{-18})^{\frac{1}{6}})$

$=3(x^{\frac{3}{6}})(y^{\frac{-18}{6}})$

$=3(x^{\frac{1}{2}})(y^{-3})$

$=\frac{3\sqrt{x}}{y^3}$

Therefore $(729x^3y^{-18})^{\frac{1}{6}}=\frac{3\sqrt{x}}{y^3}$

Therefore Option A) is correct

That is $(729x^3y^{-18})^{\frac{1}{6}}=\frac{3\sqrt{x}}{y^3}$

3 0

3 years ago

sally has 20 coins in her piggy bannk, all dimes and quarters. the total amount of money is $3.05. how many of each coin does sh

VMariaS [17]

D=dimes
q=quarters

d + q = 20
.10d + .25q = 3.05

d=-q + 20

.10(-q + 20) +.25q = 3.05
-.10q + 2 + .25 = 3.05
.15q + 2 = 3.05
.15q + 2 - 2 = 3.05 - 2
.15q = 1.05
.15q/.15 = 1.05/.15
q = 7

d + 7 = 20
d + 7 - 7 = 20 - 7
d = 13

Sally has 7 quarters and 13 dimes.
Hope this helps!

5 0

3 years ago

The difference between two numbers is 10 and their sum is 24.Find the numbers

Nezavi [6.7K]

Answer:

7 and 17

Step-by-step explanation:

24-10=14

14/2=7

7+10=17

therefore 17 and 7

7 0

3 years ago

A shipment of 20 DVDs has arrived at a video rental store. Based on past experience, the manager knows that 10% of all new DVDs

aleksley [76]

Answer:

The probability is 0.081

Step-by-step explanation:

Here, we want to calculate the probability that the 3rd inspection will be defective.

What this means is that the first two would

not be defective.

Probability of having a defective DVD = 10% = 10/100 = 0.1

Probability of not having a defective DVD = 1 -0.1 = 0.9

So the probability of third being defective = Probability of first not defective * Probability of second not defective * Probability of third defective

= 0.9 * 0.9 * 0.1 = 0.081

7 0

3 years ago

Expand and combine like terms (3z^5 +7z^2)^2

AVprozaik [17]

Answer:

$\displaystyle{(3z^5+7z^2)^2 = 9z^{10}+42z^7 + 49z^4 }$

Step-by-step explanation:

Since it's a perfect square, we can simply use the formula:

$\displaystyle{(ax+by)^2 = a^2x^2+2abxy+b^2y^2}$

Given the perfect square expression $\displaystyle{(3z^5+7z^2)^2}$ . Apply perfect square formula:

$\displaystyle{(3z^5+7z^2)^2 = 3^2(z^5)^2+2(3)(7)(z^5)(z^2) + 7^2(z^2)^2 }$

Knowing laws of exponent is mandatory when it comes to algebra. Recall that:

$\displaystyle{(a^m)^n = a^{mn}}\\\\\displaystyle{a^m \cdot a^n = a^{m+n}}$

Apply laws of exponent to simplify the terms or expression:

$\displaystyle{(3z^5+7z^2)^2 = 9z^{10}+42z^7 + 49z^4 }$

Since there are no like-terms to do operation with (these terms have different degrees so they are not considered to be like-terms.) Therefore, the final answer is:

$\displaystyle{(3z^5+7z^2)^2 = 9z^{10}+42z^7 + 49z^4 }$

8 0

1 year ago