Simplify the Expression: b^10 × b^-5 ÷ (b^11/b^6)

To simplify the expression $b^{10} \times b^{-5} \div \frac{b^{11}}{b^6}$, we will follow a systematic approach.

First, simplify the numerator:

• We have $b^{10} \times b^{-5}$. Using the rule for multiplying powers with the same base, we get:

$b^{10 + (-5)} = b^{5}$

Next, simplify the expression in the denominator:

• The denominator is $\frac{b^{11}}{b^6}$. Using the rule for dividing powers with the same base, we have:

$b^{11 - 6} = b^{5}$

Now, divide the simplified numerator by the simplified denominator:

$\frac{b^5}{b^5} = b^{5-5} = b^0$

We know that any non-zero number raised to the power of 0 is 1, therefore:

$b^0 = 1$

Therefore, the simplified expression is $1$.