Question

what is the corresponding rule for
b^5/b^10

a 5^-3
b (a^m)^n=a^mn
c (2a^4)^3

Answer 1

To simplify the expression \( \frac{b^5}{b^{10}} \), you can use the rule of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).

Applying this rule:

\[
\frac{b^5}{b^{10}} = b^{5-10} = b^{-5}
\]

Now, if you want to express this in terms of a positive exponent, you can write:

\[
b^{-5} = \frac{1}{b^5}
\]

Now, regarding the corresponding rules you provided:

a. \( 5^{-3} \) isn't directly related to your given expression, unless specified in a particular way.
b. \( (a^m)^n = a^{mn} \) is a rule for powers that doesn't apply here since we are dividing rather than raising to a power.
c. \( (2a^4)^3 \) is also a different rule for dealing with powers.

None of the provided rules directly correspond to the simplification of \( \frac{b^5}{b^{10}} \), but you could use the general rule on exponents, which is similar to the first one mentioned. If looking for a specific one from the list, option (b) is about powers, though it doesn't apply to the division you asked about.

The final answer for your original expression is:

\[
\frac{b^5}{b^{10}} = b^{-5} = \frac{1}{b^5}
\]