Question

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