Simplify and express in exponential form: 8^-1 * 3^3/ 2^-4 * 9^-2

Mathematics

2 answers:

Yuri [45]3 years ago

5 0

Answer:

2^1* 3^7

Step-by-step explanation:

8^-1 * 3^3/ 2^-4 * 9^-2

Negative exponents move from the numerator to the denominator or from the denominator to the numerator

2^4*9^2* 3^3 /8^1

Rewriting 9^2 as 3^2^2 = 3^4 and 8 = 2^3

2^4 * 3^3 * 3^4 / 2^3

2^4/ 2^3 = 2 and 3^3 * 3^4 = 3^(3+4) = 3^7

2* 3^7

sashaice [31]3 years ago

3 0

Answer:

Step-by-step explanation:

$\frac{8^{-1}*3^{3}}{2^{-4}*9^{-2}}=\frac{(2^{3})^{-1} * 3^{3}}{2^{-4}*(3^{2})^{-2}}\\\\=\frac{2^{3*-1}*3^{3}}{2^{-4}*3^{2*-2}}\\\\=\frac{2^{-3}*3^{3}}{2^{-4}*3^{-4}}\\\\=2^{-3+4}*3^{3+4}\\\\=2^{1}*3^{7}\\\\=2*3^{7}$

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Quadrilateral ABCD has the following vertices:

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Answer:

yes

Step-by-step explanation:

The figure can be shown to be a parallelogram by showing the sum of endpoints of the diagonals is the same.

A +C = B +D

(0, 6) +(0, -4) = (0, 2) = (3, 5) +(-3, -3) . . . . diagonals bisect each other

If the diagonals of a quadrilateral bisect each other, it is a parallelogram. A parallelogram with a right angle is a rectangle. So, ABCD is a rectangle.

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<em>Additional comment</em>

The midpoint of each diagonal is half the sum of the end point coordinates. That is, the midpoints are (0, 2)/2 = (0, 1). Since calculation of the midpoints requires both sums be divided by 2, we can tell the midpoints are the same if the sums are the same.