Simplifying Expressions Involving Radicals Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers. frac{sqrt[4]{x^{7}}}{sqrt[4]{x^{3}}}

Khaleesi Herbert

Khaleesi Herbert

Answered question

2020-12-30

Simplifying Expressions Involving Radicals Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
4{x7}4{x3}

Answer & Explanation

Anonym

Anonym

Skilled2020-12-31Added 108 answers

Step 1
For any rational exponent mn in lowest terms, where m and n are integers and n>0, we define
amn=(n{a})m=n{am}
If n is even, then we require that a0
Step 2
Consider the given expression,
4{x7}4{x3}
By using the law of exponents,
4{x7}4{x3}=x74x34
Apply exponent rule: xaxb=xab, we get
x74x34=x7434
=x44
=x
Final Statement:
The simplified form of 4{x7}4{x3} is x.

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