Question

Simplify fraction 10b²c² / c³√8b⁴

Answer 1

The simplified form of the expression is
`\((5b)/(c)\).`

Explanation:

To simplify the expression
`\(\frac{10b^2c^2}{c^{(3)/(2)}√(8b^4)}\),` start by breaking down the denominator using exponent rules. The cube root of
`\(8b^4\)` can be rewritten as
`\(\sqrt[3]{8}*√(b^4)\),` which simplifies to
`\(2b^2\)` . Now, substitute this simplified form into the original expression:

`\(\frac{10b^2c^2}{c^{(3)/(2)}√(8b^4)} = \frac{10b^2c^2}{c^{(3)/(2)}* 2b^2}\)`

Next, simplify the expression by canceling out common factors in the numerator and denominator. Reduce the exponents of \(b\) and \(c\):

`\(\frac{10b^2c^2}{c^{(3)/(2)}* 2b^2} = \frac{10b^2c^2}{2b^2c^{(3)/(2)}}\)`

Further simplify by canceling out common terms: \(2\) from the numerator and denominator,
`\(b^2\)` from the numerator and denominator, and
`\(c^{(3)/(2)}\)` from the denominator:

`\(\frac{10b^2c^2}{2b^2c^{(3)/(2)}} = \frac{5c^{(1)/(2)}}{1}\)`

Finally, simplify
`\(c^{(1)/(2)}\) to \( √(c)\),` giving the final simplified expression:

`\(\frac{5c^{(1)/(2)}}{1} = 5√(c) = (5b)/(c)\)`

Answer 2

The simplified form of the fraction
`\( \frac{10b^2c^2}{c^3\sqrt[3]{8b^4}} \)` is
`\( \frac{5}{\sqrt[3]{2b^2}} \).`

Step-by-step explanation:

To simplify the given fraction, we can start by factoring the terms in the denominator. The expression
`\( \sqrt[3]{8b^4} \)`can be expressed as
`\( \sqrt[3]{2^3 \cdot (b^2)^2} \)`, which simplifies to
`\( 2b^2 \)`. Substituting this into the original fraction, we get
`\( (10b^2c^2)/(c^3 \cdot 2b^2) \).`

Next, we can simplify further by canceling out common factors in the numerator and denominator. Canceling
`\( b^2 \)` in the numerator and denominator leaves us with
`\( (10c^2)/(c^3 \cdot 2) \)`.

Now, we simplify the expression by subtracting the exponents in the denominator, giving
`\( \frac{5}{\sqrt[3]{2b^2}} \)`. The final answer is
`\( \frac{5}{\sqrt[3]{2b^2}} \)`, where the radical is in the denominator.

In summary, we simplified the fraction by factoring the cube root in the denominator, canceling common factors, and then subtracting exponents. The final result is
`\( \frac{5}{\sqrt[3]{2b^2}} \)`), a simplified expression of the original fraction.