Express each of the following as a single fraction involving positive exponents

zi2lalZ

zi2lalZ

Answered question

2021-10-04

Express each of the following as a single fraction involving positive exponents only.
3a2+4b1

Answer & Explanation

broliY

broliY

Skilled2021-10-05Added 97 answers

Step 1 
By taking the reciprocal of the relevant term, the negative exponents can be changed to positive exponents.
We can use the format xn=1xn to convert the negative exponents to positive exponents. 
We can write x2 as 1x2 using the format xn=1xn 
Step 2 
Consider the expression 3a2+4b1 
First, we must change the expression's negative exponents to positive exponents by using the form xn=1xn 
The we get the expression as 
3a2+4b1=3×1a2+4×1b 
3a2+4b1=3a2+4b 
Now we have to solve the fractions to get the single fractional form. We have to find the LCM(LCD) of the denominators of the fractions and we need to convert both the denominators to the LCM value by multiplying with the constant number or expression. 
Here we have LCM(least common multiple) of a2 and b is a2b, we have to convert both denominators of fractions to a2b 
Thus we get 
3a2+4b=3a2×bb+4b×a2a2 
=3ba2b+4a2a2b 
=3b+4a2a2b 
Hence we have the single fractional form 4a2+3ba2b

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