What is the expression in radical form? (5x^3 y^2) 2/8

1 answer:

8 0

Answer: (y^{2}x^{3}⋅5)/4

Step-by-step explanation:

Convert to Radical Form

$(5x^3y^2)\frac{2}{8}$

Reduce the expression $\frac{2}{8}$ by cancelling the common factors.

Factor 2 out of 2.

$5x^3y^2\frac{2(1)}{8}$

Factor 2 out of 8.

$5x^3y^2 \frac{2(1)}{2(4)}$

Cancel the common factor.

$5x^3y^2 \frac{1}{4}$

Combine 5 and $\frac{1}{4}$ .

$x^3y^2\frac{5}{4}$

Combine $x^{3}$ and $\frac{5}{4}$ .

$y^2\frac{x^3(5)}{4}$

Combine $y^{2}$ and $\frac{x^3*5}{4}$

$\frac{y^2x^3*5}{4}$

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Using the rational root theorem, it is found that your friend is correct.

<h3>What is the rational root theorem?</h3>

It is a theorem that states that for a polynomial with integer coefficients, with q being the factors of the leading coefficient and p being the factors of the constant, every <u>possible rational root</u> is the format $\frac{p}{q}$ .

In this problem:

The leading coefficient is 1, hence it's only factor is $q = 1$ , thus guaranteeing that every possible rational zero is an integer, which means that your friend is correct.