How do I simplify fractions with exponents?

In summary, the equation (2x+3x)/6x = 2-x+3-x can be solved by splitting the left side into two fractions and then flipping them over and making the exponent -x. This will simplify the equation and make it easier to solve.
  • #1
Aerospace93
22
0

Homework Statement


(2x+3x)/6x = 2-x+3-x

I've tried moving the 6 above, splitting it up and so... but i can't figure how to do it. It must be pretty simple, but I am just not seeing it. all helps appreciated!
 
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  • #2
Aerospace93 said:

Homework Statement


(2x+3x)/6x = 2-x+3-x

I've tried moving the 6 above, splitting it up and so... but i can't figure how to do it. It must be pretty simple, but I am just not seeing it. all helps appreciated!

Start by "splitting" the left side into two fractions, like this:
[tex]\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}[/tex]
 
  • #3
i certainly did that
 
  • #4
(1/2)^x+(1/3)^x... which is the same as flipping them over and making the exponential -x. cool
 

Related to How do I simplify fractions with exponents?

What are exponents and why do we use them?

Exponents are a mathematical notation that represents repeated multiplication. They are used to make calculations with large numbers more efficient and to express numbers in a simpler form.

How do you simplify expressions with exponents?

To simplify an expression with exponents, you can use the rules of exponents. These rules include multiplying exponents with the same base, dividing exponents with the same base, and raising a power to a power. You can also use the rule for zero exponents, which states that any number raised to the power of 0 is equal to 1.

What is the difference between positive and negative exponents?

Positive exponents indicate that the base is multiplied by itself a certain number of times, while negative exponents indicate that the base is divided by itself a certain number of times. For example, 53 is equal to 5 x 5 x 5, while 5-3 is equal to 1 ÷ 5 ÷ 5 ÷ 5.

Can exponents be fractions or decimals?

Yes, exponents can be fractions or decimals. For example, 21/2 is equal to the square root of 2, and 30.5 is also equal to the square root of 3. Exponents can also be negative fractions or decimals, such as 2-1/2 which is equal to 1 ÷ √2.

How can we use exponents in real life?

Exponents are used in many areas of science, such as physics, chemistry, and biology. They are also used in finance and economics to calculate compound interest and growth rates. In everyday life, we can use exponents to solve problems involving large numbers, such as calculating the number of bacteria in a petri dish or the distance traveled by a rocket.

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