1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tresset_1 [31]
3 years ago
10

Prove the divisibility:45^45·15^15 by 75^30

Mathematics
1 answer:
garri49 [273]3 years ago
7 0

Answer:

3^{75}.

Step-by-step explanation:

We have been an division problem: \frac{45^{45}*15^{15}}{75^{30}}.

We will simplify our division problem using rules of exponents.

Using product rule of exponents (a*b)^n=a^n*b^n we can write:

45^{45}=(9*5)^{45}=9^{45}*5^{45}

15^{15}=(3*5)^{15}=3^{15}*5^{15}

75^{30}=(15*5)^{30}=15^{30}*5^{30}

Substituting these values in our division problem we will get,

\frac{9^{45}*5^{45}*3^{15}*5^{15}}{15^{30}*5^{30}}

Using power rule of exponents a^n*a^m=a^{n+m} we will get,

\frac{9^{45}*5^{(45+15)}*3^{15}}{15^{30}*5^{30}}

\frac{9^{45}*5^{60}*3^{15}}{15^{30}*5^{30}}

Using product rule of exponents (a*b)^n=a^n*b^n we will get,

\frac{(3*3)^{45}*5^{60}*3^{15}}{(3*5)^{30}*5^{30}}

\frac{3^{45}*3^{45}*5^{60}*3^{15}}{3^{30}*5^{30}*5^{30}}

Using power rule of exponents a^n*a^m=a^{n+m} we will get,

\frac{3^{(45+45+15)}*5^{60}}{3^{30}*5^{(30+30)}}

\frac{3^{105}*5^{60}}{3^{30}*5^{60}}

\frac{3^{105}}{3^{30}}

Using quotient rule of exponent \frac{a^m}{a^n}=a^{m-n} we will get,

\frac{3^{105}}{3^{30}}=3^{105-30}

3^{105-30}=3^{75}

Therefore, our resulting quotient will be 3^{75}.

You might be interested in
Name the angle in (4) different ways.
MaRussiya [10]

Answer:

An angle can be named in different ways:

•by a number or letter written inside the angle.

•by the name of the vertex.

•by the vertex and a point on each ray.

3 0
3 years ago
How to measure and find the circumcenter of a triangle
Nadusha1986 [10]
Circumcenter Calculator

Circumcenter of triangle can be defined as the point where the three perpendicular bisectors of the sides of the triangle meet. The distance of vertices of triangle is equal to circumcenter.

It is the single point where the perpendicular bisectors of the three sides of the triangles meet .
It is basically the point of concurrency inside the triangle.
The distance of circumcenter from the three vertices of triangle are equal.
It is used to draw the circum circle , infact it is the center of the circumcircle formed.
There is a unique circumcenter possible for each and every triangle.
Circumcenter Calculator is used to calculate the circumcenter of the triangle, if three coordinates are given.
Please mark braileist I only need one
4 0
3 years ago
Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution
docker41 [41]

Answer:

D. No, because the differential equation does not have constant coefficients.

Step-by-step explanation:

The undetermined coefficient method cannot be applied to non homogeneous variables. The differential equation does not have constant variables therefore the method of undetermined superposition can not be applied. To complete a solution of non homogeneous equation the particular solution must be added to the homogeneous equation.

6 0
3 years ago
Multiply (-3a + 4b) by 5a.​
Tasya [4]

Answer:

-15a^2+20ab

Step-by-step explanation:

Given data

We are given the expression

(-3a + 4b) to be multiplied by 5a

hence we have

(-3a + 4b)*5a

open bracket

-15a^2+20ab

Hence the answer is

-15a^2+20ab

7 0
3 years ago
Kim purchased 6 small containers of potato salad and Seth purchased 2 extra large containers of potato salad. What is the differ
icang [17]

I am assuming that the attached is the complete question and we need to get the information from the table.

From the table we know the below fact:

1 \; small \; container \; of \; potato \; salad \; Weighs \; \frac{2}{8} \; pounds\\\\1 \; extra \; large \; container \; of \; potato \; salad \; Weighs \; \frac{9}{8}  \; pounds

Weight \; of \; 6 \; small \; container = 6 \times \frac{2}{8}  = \frac{12}{8}  \; pounds\\\\Weight \; of \; 2 \; Extra \; large \; container = 2 \times \frac{9}{8} \; = \; \frac{18}{8}  \; pounds

Conclusion:

The difference in weights, in pounds of Kim’s and Seth’s purchases is given below:

\frac{18}{8} - \frac{12}{8} =  \frac{18-12}{8}   = \frac{6}{8}  \\\\Simplifying \; the \; fraction \; dividing \; by \; 2 \; on \; both \; numerator \; and \; denominator\\\\ \frac{6 \div 2}{8 \div 2}  = \frac{3}{4}

Final answer : <em><u>0.75 pounds</u></em>

6 0
3 years ago
Read 2 more answers
Other questions:
  • Shamariah collects silk roses. She had 17 silk roses in a vase. Six friends each gave her 3 more roses. How many roses does sham
    14·1 answer
  • A nutrition label indicates that one serving of Apple crisp oatmeal has 2.5 grams of fat. How many grams of fat are there in 3.7
    12·1 answer
  • What fraction is equal to the decimal 0.32
    9·2 answers
  • Given that Ray E B bisects ∠CEA, which statements must be true? Select three options.
    13·1 answer
  • How to combine like terms
    10·2 answers
  • Lori needs more than 250 signatures to run for the position of class president for her middle school. She already has 75 signatu
    7·1 answer
  • Explain the error in the solution below. What
    10·1 answer
  • Can someone please help me with these two questions? I would be really grateful...
    8·1 answer
  • Jacob performs the work shown to find tan Tangent 165 degrees. Tangent 165 degrees = negative StartRoot StartFraction 1 + cosine
    11·2 answers
  • 7, 11, 2, 18, -7, __ find the missing pattern.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!