Simplify.
Rewrite the expression in the form
\[b^n\].
\[\dfrac{b^{10}}{b^6}=\]
We can simplify this expression by using the rule $b^m/b^n = b^{m-n}$. Applying this rule to the given expression, we have \[\frac{b^{10}}{b^6} = b^{10-6}=b^4.\] Thus, the expression is simplified to $\boxed{b^4}$.
We can rewrite $a\cdot a^7$ as $a^1\cdot a^7$.
Using the rule $a^m\cdot a^n = a^{m+n}$, we can simplify this to $a^{1+7}=a^8$.
Therefore, the expression is equivalent to $\boxed{a^8}$.
Simplify.
Rewrite the expression in the form
\[a^n\].
\[a\cdot a^7=\]
To simplify the given expression \(\dfrac{b^{10}}{b^6}\) and rewrite it in the form \(b^n\), we can use the property of exponents which states that when dividing two terms with the same base, we subtract the exponents.
Here's how you can simplify it step by step:
Step 1: Using the exponent subtraction property, subtract the exponent of \(b\) in the denominator from the exponent of \(b\) in the numerator.
\(\dfrac{b^{10}}{b^6} = b^{10-6}\)
Step 2: Simplify the exponent.
\(b^{10-6} = b^4\)
So, the expression \(\dfrac{b^{10}}{b^6}\) simplifies to \(b^4\).
Therefore, \(\dfrac{b^{10}}{b^6} = b^4\).