Question

Write each expression with a single rational exponent. Show each step of your process. Which expressions are equivalent? Justify your reasoning.


fourth root of x cubed
one over x to the negative one power
tenth root of the quantity x to the fifth times x to the fourth times x squared
x to the one third power times x to the one third power times x to the one third power

Answer 1

The expression of all the algebra as single rational exponent are; As written below.

How to Express Exponents?

1) We want to express ⁴√x³. This can be expressed as;

x^(3/4)

2) We want to express the exponent ¹/x⁻¹. This is expressed as a single rational exponent as; x

3) We want to have the given expression as a single rational exponent. The expression is; ¹⁰√(x⁵ · x⁴ · x²)

We add the exponents to get;

¹⁰√(x¹¹) = x^(¹¹/₁₀)

4) x^(¹/₃) * x^(¹/₃) * x^(¹/₃)

We just add the exponents to get;

x¹ = x

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