Rewrite each expression so that each term is in the form kx^{n}, where k is a real number, x is a positive real number, and n is a rational number. a)x^{-frac{2}{3}} times x^{frac{1}{3}}=? b) frac{10x^{frac{1}{3}}}{2x^{2}}=? c) (3x^{frac{1}{4}})^{-2}=?

shadsiei

shadsiei

Answered question

2021-02-05

Rewrite each expression so that each term is in the form kxn, where k is a real number, x is a positive real number, and n is a rational number.
a)x23 × x13=?
b) 10x132x2=?
c) (3x14)2=?

Answer & Explanation

liingliing8

liingliing8

Skilled2021-02-06Added 95 answers

First, we must reformat the supplied statement to take the form of kxn. 
To simplify an equation, we must first understand the exponents rule.
1. am × an=am + n 
2. aman=am  n 
3. (am)n=a(m × n) 
We shall now rephrase the expression that was supplied.
(a) Expression is x23 × x13 
We shall now rephrase the expression that was supplied.
x23 × x13=x(23 + 13) 
=x(2 + 13) 
=x13 
(b) Expression is 10x132x2. 
The following expression can be written:
10x132x2=102 × x13 × x2 
=5x(12  2) 
=5x1  63 
=5x53 
(c) Expression is (3x14)2 
You can write the above expression as:
(3x14)2=3x14 × 2 
=3x12

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