Question

Simplify this expression. Assume that b and h are both nonzero.
StartFraction 5 b Superscript 6 Baseline h Superscript 5 Over 30 b Superscript 6 Baseline h squared EndFraction
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Part 1
StartFraction 5 b Superscript 6 Baseline h Superscript 5 Over 30 b Superscript 6 Baseline h squared EndFraction
equals
  
enter your response here ​(Type your answer using exponential​ notation.)

Answer 1

To simplify the expression

\[
\frac{5 b^6 h^5}{30 b^6 h^2},
\]

we can start by simplifying the coefficients and the variables separately.

1. **Coefficients:** The numerator has 5 and the denominator has 30. We can simplify this as follows:

\[
\frac{5}{30} = \frac{1}{6}.
\]

2. **For \(b^6\):** In the numerator and denominator, we have \(b^6\) in both. When we divide \(b^6\) by \(b^6\), we get:

\[
\frac{b^6}{b^6} = 1.
\]

3. **For \(h\):** The numerator has \(h^5\) and the denominator has \(h^2\). When you divide powers of the same base, you subtract the exponents:

\[
\frac{h^5}{h^2} = h^{5-2} = h^3.
\]

Putting it all together, we have:

\[
\frac{5 b^6 h^5}{30 b^6 h^2} = \frac{1}{6} \cdot 1 \cdot h^3 = \frac{h^3}{6}.
\]

Thus, the simplified expression is:

\[
\frac{h^3}{6}.
\]

In exponential notation, this can also be written as:

\[
\frac{1}{6} h^3.
\]

So, the final answer is:

\[
\frac{h^3}{6}
\] or equivalently \(\frac{1}{6} h^3\).