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2 years ago

Rewrite the problem. Multiply and reduce if needed. Use the (') as the divisor li

Mathematics

1 answer:

Alik [6]2 years ago

8 0

Answer:

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Step-by-step explanation:

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

Anuta_ua [19.1K]

Answer:

$3^{75}$

Step-by-step explanation:

We are asked to divide our given fraction: $\frac{45^{45}*15^{15}}{75^{30}}$ .

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:

$45^{45}=(3*15)^{45}=3^{45}*15^{45}$

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

Substituting these values in our division problem we will get,

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

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

$\frac{3^{45}*15^{45+15}}{5^{30}*15^{30}}$

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

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

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

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

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

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

$\frac{3^{45}*3^{30}*5^{30}}{5^{30}}$

Upon canceling out $5^{30}$ we will get,

$3^{45}*3^{30}$

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

$3^{45+30}$

$3^{75}$

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

8 0

2 years ago

The measurement of a central angle is 75. Find the measurement of in radians

Marina CMI [18]

Circumference = 360 degrees
Circumference = 2π radians (comes from 2*pi*radius) 

Therefore 
360 deg. = 2*π radians 
180 deg. = π radians 
1 deg. = (π/180) radians 

75 deg. = 75(π/180) radians 
75 deg. = 75π / 180 radians 
don't bother to try and simplify π (it is an irrational number) 
however you can simplify 75/180 
both are divisible by 5 
75π/180 = 15π/36 
both are divisible by 3 
75 deg. = 5π/12 radians 

We normally don't bother to go further, unless you actually need it as a decimal fraction (in which case, you will have an approximation) 

75 deg. ≈ 1.308997 radians

5 0

3 years ago

In my defense, I was never good at math.

Annette [7]

Answer:

-3/2

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

What is greater 1/4 or 0.4?

Alik [6]

1/4 in decimal form is 0.25, so 0.4 is definitely greater.

4 0

2 years ago

X-124=9(2x+3)-15 ???

musickatia [10]

Answer:

x = - 8

Step-by-step explanation:

x - 124 = 9(2x + 3) - 15

x - 124 = 18x + 27 - 15

x - 124 = 18x + 12

x - 124 + 124 = 18x + 12 + 124

x = 18x + 136

x - 18x = 18x - 18x + 136

- 17x = 136

- 17x ÷ - 17 = 136 ÷ - 17

x = - 8

8 0

2 years ago