Simplify the expression. $$ \frac{\mathrm{b}^{2}}{\mathrm{~b}^{7}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{b^{2}}{b^{7}}
$$

we can use the **laws of exponents**. Specifically, when dividing two expressions with the same base, you subtract the exponents:

$$
\frac{b^{m}}{b^{n}} = b^{m - n}
$$

Applying this rule to your expression:

$$
\frac{b^{2}}{b^{7}} = b^{2 - 7} = b^{-5}
$$

A negative exponent indicates the reciprocal of the base raised to the positive exponent. Therefore:

$$
b^{-5} = \frac{1}{b^{5}}
$$

**Final Answer:**

$$
\frac{1}{b^{5}}
$$
$$ \frac{1}{b^{5}} $$

Simplify the expression.