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3 years ago

Find the LCM of the numbers using prime factorizations. 36,60

Mathematics

1 answer:

alexandr402 [8]3 years ago

5 0

36=2*2*3*3=2²*3²
60=2*2*3*5=2²*3*5

LCM(36,60)=2*2*3*3*5=2²*3²*5=180

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Use the rules of exponents to simplify the expressions. Match the expression with its equivalent value.

Lelechka [254]

Answer:

1) $\frac{(-2)^{-5}}{(-2)^{-10}}=-32$

2) $2^{-1}.2^{-4} = \frac{1}{32}$

3) $(-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}$

4) $\frac{2}{2^{-4}} = 32$

Step-by-step explanation:

1) $\frac{(-2)^{-5}}{(-2)^{-10}}$

Solving using exponent rule: $a^{-m}=\frac{1}{a^m}$

$\frac{(-2)^{-5}}{(-2)^{-10}}\\=(-2)^{-5+10}\\=(-2)^{5}\\=-32$

So, $\frac{(-2)^{-5}}{(-2)^{-10}}=-32$

2) $2^{-1}.2^{-4}$

Using the exponent rule: $a^m.a^n=a^{m+n}$

We have:

$2^{-1}.2^{-4}\\=2^{-1-4}\\=2^{-5}$

We also know that: $a^{-m}=\frac{1}{a^m}$

Using this rule:

$2^{-5}\\=\frac{1}{2^5}\\=\frac{1}{32}$

So, $2^{-1}.2^{-4} = \frac{1}{32}$

3) $(-\frac{1}{2} )^3.(-\frac{1}{2} )^2$

Solving:

$(-\frac{1}{2} )^3.(-\frac{1}{2} )^2\\=(-\frac{1}{8} ).(\frac{1}{4} )\\=-\frac{1}{32}$

So, $(-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}$

4) $\frac{2}{2^{-4}}$

We know that: $a^{-m}=\frac{1}{a^m}$

$\frac{2}{2^{-4}}\\=2\times 2^4\\=2(16)\\=32$

So, $\frac{2}{2^{-4}} = 32$

3 0

3 years ago

the sales tax for the food Jordan bought is 0.87 she has a coupon for 1.75 off any purchase use your answer for exercise 16 to f

krok68 [10]

Related to ur last question......food totaled 17.42

17.42 - 1.75 = 15.67...this is with the coupon added
15.67 + 0.87 = 16.54....this is the final total....with tax included

so ur answer is 16.54

3 0

3 years ago

Read 2 more answers

brooklyn bought 8 bags of the same dog food. She has a $5 coupon. She spent $91. How much was each bad of dog food?

blsea [12.9K]

Answer:

$12

Step-by-step explanation:

Hi there!

What we know:

Brooklyn bought 8 bags of dog food
Brooklyn also used a $5 coupon
The total was $91

Therefore, 8 × (cost of 1 bag) - 5 = 91

Form an equation with x as the cost of 1 bag of dog food:

8 × (cost of 1 bag) - 5 = 91

$8x-5=91$

Add 5 to both sides

$8x-5+5=91+5\\8x=96\\$

Divide both sides by 8

$\frac{8x}{8} = \frac{96}{8} \\x=12$

Therefore, 1 bag of dog food costs $12.

I hope this helps!

5 0

3 years ago

If the baker’s percentage for raisins in a raisin bread formula is 8% and the baker’s percentage for flour is 100%, what amount

svet-max [94.6K]

Answer: 1.12 pounds.

Step-by-step explanation:

1. You have the following information given in the problem above:

-The baker’s percentage for raisins in a raisin bread formula is 8%.

-The baker’s percentage for flour is 100%

2. Therefore, the amount of raisins that are needed if 14 pounds of flour are used is:

$\frac{(14)(8)}{100}=1.12$ pounds

3 0

3 years ago

2(x - 6) Use Distribution

Galina-37 [17]

To distribute you first need to multiply 2 by x which equals 2x. Then you need to multilply 2 by -6 and that equals -12. Your final answer would be 2x-12

8 0

3 years ago

Read 2 more answers