Beginning Algebra With Applications, Chapter 7, 7.2, Section 7.2, Problem 42

a. True or false? $a^2 b^5 = ab^{10}$

The statement is false because you can't add exponent with different base.

b. True or false? $a^2 b^5 = ab^7$

The statement is false because you can't add exponent with different base.

c. True or false? $(a^2 b^5) = a^4 b^{25}$

The statement is false. We know that the rule for simplifying powers of product $(x^m)^n = x^{mn}$.

d. True or false? $(a^2 + b^5)^2 = a^4 + b^{10}$

The statement is false because the expression in the left side is an example of a square of a binomial and it is not equal to the expression in the right side.