Question

what is its corresponding rule
a^m a^n = a^(m+n)
what is the correct answer
a 5^-3
b (a^m)^n=a^mn
c (2a^4)^3
d x^5 • x^8

Answer 1

The rule \( a^m a^n = a^{m+n} \) represents the property of exponents that states when you multiply two exponential expressions with the same base, you can add their exponents.

Among the choices you provided, the one that corresponds to this rule is:

**d) \( x^5 \cdot x^8 \)**

This expression uses the same base \( x \), and applying the rule \( a^m a^n = a^{m+n} \), it simplifies to \( x^{5+8} = x^{13} \).

The other choices do not directly represent the same exponent multiplication rule:

- a) \( 5^{-3} \) does not involve any addition of exponents with like bases.
- b) \( (a^m)^n = a^{mn} \) is a different exponent rule (power of a power).
- c) \( (2a^4)^3 \) involves multiplication by a coefficient and requires applying the distributive property of exponents, which is also not the same rule.

So, the correct answer is indeed **d) \( x^5 \cdot x^8 \)**.