Which statement is true?

When (81x^2/7) (2/9x^3/7) is simplified, it can be written in the form ax^b where a and b are real numbers. Find ab.

larisa86 [58]

Answer:

In improper form your solution will be $\frac{90}{7}$ . As a mixed fraction it will be $12\frac{6}{7}$ .

Step-by-step explanation:

The first thing we want to do here is to simplify this expression. After doing so, " a " and " b " should be multiplied to result in a possible improper fraction,

$\left(81x^{\frac{2}{7}}\right)\:\left(2/9x^{\frac{3}{7}}\right)\:$ - Apply exponential rule " $\:a^b\cdot \:a^c=a^{b+c}$ "

= $81\cdot \frac{2}{9}x^{\frac{2}{7}+\frac{3}{7}}$ - Combine fractions $\frac{2}{7}$ and $\frac{3}{7}$

= $81\cdot \frac{2}{9}x^{\frac{5}{7}}$ - Multiply the fractions, and simplify further

= $\frac{162x^{\frac{5}{7}}}{9}$ = $18x^{\frac{5}{7}}$ - This is out simplified expression

Now that we have this simplified expression, we can see that a = $18$ , and b = $\frac{5}{7}$ . Therefore, multiplying the two we should receive the improper fraction as follows,

$18 * \frac{5}{7}$ = $\frac{90}{7}$ - Note that this is in improper form. If you want your solution in a mixed fraction, it will be $12\frac{6}{7}$ .

5 0

4 years ago

GIFT SHOP A gift shop sells souvenir magnets. The store is selling 3 magnets for $10. At this price, how much will it cost to bu

zaharov [31]

£26.4 because 10÷3 is 3.3 requiring and 3.3×8 is 26.4

3 0

3 years ago

(05.07) The net of a pyramid is shown below.

mote1985 [20]

Hey. Let me help you on this one.

In order for us to solve this question, we need to break this problem apart. It will make it easier to understand.

In this problem, we see five different figures - four triangles, and one square.

If we want to get the complete net-surface area, we will need to find area of each figure individually, and then, add all values together.

Let's start with a square in the center. Formula for area of a square is $S=a*a$ . In this formula, $S$ stands for total area of a square, and stands for the length of one side.

Let's substitute the values!
$S=4*4$
$S=14$

Area of the square is 14 inches squared. Awesome! Now, let's find the area of all triangles.

We can see that one of the triangles has both measures - base, and the height. We need these two values in order for us to find the measure of the triangles.

Formula for the area of a triangle is $S= \frac{a*b}{2}$ . So, we need to multiply base length by the height length, and divide by two.

$S= \frac{4*8}{2}$
$S= \frac{32}{2}$
$S=16$

Now, we know the area of one triangle. We have three other identical triangles, and in order for us to save time, let's just multiply this number by four.
$16*4=64$

Triangles are 64 inches squared in total.
64 inches squared + 14 inches squared (square area) equals to 78 inches squared.
Answer: $78^{2}$ is the area of the figure

8 0

3 years ago

If Joe earns $25 per hour during a normal week (40 hours per week), but earns $37.50 per overtime, how much does he earn in 48 h

Svetradugi [14.3K]

Answer:

1300

Step-by-step explanation:

Regular time is 40 hours at 25 dollars per hour

Regular pay is 40*25 = 1000

He worked 48 hours, 48-40 =8, so he worked 8 hours overtime

8 hours at 37.50 overtime pay

8*37.50=300

His total pay is regular pay plus overtime pay

1000+300 = 1300

4 0

4 years ago

What is the measure of ZABC?*

gtnhenbr [62]

Answer:

d)58

Step-by-step explanation:

21+37=58 add angles

8 0

3 years ago

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