Question

In which expression should the exponents be multiplied?

A) ( (5^3)^-4 )
B) ( 1/3^4 times 1/3^7 )
C) ( 3/7 div 3/15 )
D) ( 4^5 cdot 4^2 )

Answer 1

The exponents should be multiplied in expression D) (4^5 · 4^2), and this is an application of the Power of a Power property in exponents.

Step-by-step explanation:

The expression in which the exponents should be multiplied is D) (45 · 42). According to the rules for dealing with exponents, when you multiply two exponents with the same base, you keep the base and add the exponents. However, in this case, since the base is the same (4), you would actually multiply the exponents (5 and 2) to make the problem easier to understand. Doing this does not change the value but simplifies the expression, giving us 45×2 or 410. This is an application of the Power of a Power property, where we multiply the exponents when raising a power to another power, a concept illustrated by the equation (ab)c = ab×c.