What are rational exponents, and how are they related to integer exponents?

See below  

Step-by-step explanation:

Integer exponents are a subset of rational exponents

Integer exponents

An integer exponent is an exponent that is an integer. For example, in the expression y = 5³, the 3 is an integer exponent.

An integer exponent is a power. Thus, 5³ = 5× 5× 5.

Rational exponents

Rational exponents can be expressed as a ratio of integers with nonzero denominators.

Thus, in the expression , the fraction ⅔ is a rational exponent.

A rational exponent is both a power and an nth root. The numerator is the power, and the denominator is the root. Thus,

"standard form:

3x2 + 14x − 10 = 0

solutions based on quadratic formula:

x1   = −14 − √ 142 − 4×3×(−10) /   2×3   = −14 − 2 × √ 79 /   6   ≈ −5.296

x2   = −14 + √ 142 − 4×3×(−10) /   2×3   = −14 + 2 × √ 79 /   6   ≈ 0.629