Express the following fraction in simplest form using only positive exponents.

Question

start fraction, 3, left parenthesis, b, squared, right parenthesis, cubed, divided by, 2, b, to the power 5 , end fraction
2b
5

3(b
2
)
3

​

Answer 1

To simplify the expression \(\frac{3(b^2)^3}{2b^5}\), we need to follow these steps:

1. Simplify the numerator: \[ (b^2)^3 = b^{2 \cdot 3} = b^6 \] Therefore, the numerator becomes: \[ 3(b^2)^3 = 3b^6 \]

2. Substitute the simplified numerator back into the fraction: \[ \frac{3b^6}{2b^5} \]

3. Now, simplify the fraction by dividing \(b^6\) by \(b^5\): \[ \frac{b^6}{b^5} = b^{6-5} = b^1 = b \]

4. Now, rewrite the fraction: \[ \frac{3}{2} \cdot b \]

So, the final simplified form of the expression is: \[ \frac{3b}{2} \]

This expresses the fraction in its simplest form using only positive exponents.