/

Simplify the expression below. Which of the following is correct? \(18x^5yz\ \div\ \ 6xyz^4\)

A. \(3x^4z^3\)

B. \(3x^4yz^3\)

C. \(\frac{(3x)^4}{z^3}\)

D. \(\frac{(3x^4)}{z^3}\)

Answer Explanation:

We use the properties of exponent with the same base to solve for above expression.

Multiplication of exponents with same base, we add the exponents

Division of exponents with same base, we subtract the exponents

Using these two properties, we can solve the expression:

Now we use the following properties:

y0 =1, and  , thus

Therefore, the Correct Answer is D.

More Questions on TEAS 7 Math

  • Q #1: A girl and a dog are playing tug of war with a piece of rope. The girl pulls on the rope with a force of 165 newtons (N) towards the east, and the dog pulls with a force of 190 N towards the west. What is the net force on the rope?

    A. 25 N towards the west

    B. 190 N towards the west

    C. 165 N towards the east

    D. 35 N towards the east

    Answer Explanation

    To find the net force, we choose east direction as positive and west as negative. From this, we can present the tag of war in the diagram below.

    So, the force on the dog is -190 N and that of the girl is 165 N.

    The net force is the sum of the two forces

    The resulting force is negative, meaning it is in the west direction. Thus, the net force is 25 N to the west.

  • Q #2: Using the numbers below, which of the following is the greatest? 4/3, 27/20, 1.369, 1.357  

    A. 1.369

    B. 4/3

    C. 27/20

    D. 1.357

    Answer Explanation

    to do a comparison of the given data set, we convert the fraction numbers into the approximate decimals.

    4/3=1.333

    2720=1.35

    Now, we have 1.333, 1.35, 1.369, 1.357. These numbers are arranged from the smallest to the largest number, we look at the number in the second decimal place value

    1.333 the number in second decimal place value is 3

    1.35 the number in third decimal place value is 5

    1.369 the number in third decimal place value is 6

    1.357 the number in third decimal place value is 5

    However, 1.35 and 1.357 have 5 in the second-place vale. We use the ird place value to compare the two number:

    1.35 is same as 1.350 and the number in the third-place value is 0

    1.357 the number in the third-place value is 7

    Now, 0 is less than 7, and thus 1.35 is less than 1.357

    Overall, 3 is less than 5, and 5 less than 6 and the provided numbers can be arranged from the smallest to the largest as:

    1.333, 1.35, 1.357, 1.369

    Thus, the corresponding given numbers organized from the smallest to the largest become:

    4/3, 27/20, 1.357, 1.369

    The greatest value is 1.369

  • Q #3: Which of the following values is the greatest?

    A. 9/2

    B. 10/3

    C. 4.4

    D. 4.25

    Answer Explanation

    We are given a mix of fractions and decimals and to compare the numbers, we convert the given decimals to fractions.

    4.4 becomes 44/10

    4.25 becomes 425/100

    Now the set of fractions for comparison are: 9/2, 10/3, 44/10, and 425/100. The least common denominator for 2, 3 and 10 is 300. Then,

    9/2*300=1350

    10/3*300=1000

    44/10*300=1320

    425/10*300=1275

    From the above products, 9/2 gives the greatest value when the fractions are compared with the least common denominator of the given denominators.