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 2021-02-05 Answered
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=?
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Expert Answer

liingliing8
Answered 2021-02-06 Author has 95 answers
Step 1
We have to rewrite the given expression in the form of kxn.
Before going to simplify expression, first we need to know about rule of exponents.
1. am × an=am + n
2. aman=am  n
3. (am)n=a(m × n)
Now, we will rewrite the given expression.
(a) Expression is x23 × x13
Given expression can be written as:
x23 × x13=x(23 + 13)
=x(2 + 13)
=x13
(b) Expression is 10x132x2.
Given expression can be written as:
10x132x2=102 × x13 × x2
=5x(12  2)
=5x1  63
=5x53
(c) Expression is (3x14)2
Given expression can be written as:
(3x14)2=3x14 × 2
=3x12
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