Answer
(a.) Yes.
(b.) No.
(c.) Yes.
Work Step by Step
(a.)
$=2^5\cdot 2$
$=2^5\cdot 2^1$
Use power rule.
$=2^{5+1}$
Simplify.
$=2^{6}$
$=64$ yes, it is correct.
(b.)
$=2^2\cdot 2^3$
Use power rule.
$=2^{2+3}$
Simplify.
$=2^{5}$
$=32$ No, it is incorrect.
(c.)
$=(2^2)( 2^2)^2$
Clear the parentheses.
$=2^2\cdot 2^{2\cdot 2}$
Simplify.
$=2^2\cdot 2^{4}$
Use power rule.
$=2^{2+4}$
Simplify.
$=2^{6}$
$=64$ yes, it is correct.
