Find the equivalent exponential expression.

[(-4)^5]^3

A.(-4)^-2
B.(-4)^8
C.(-4)^2
D.(-4)^15

Question

Find the equivalent exponential expression.

[(-4)^5]^3

A.(-4)^-2
B.(-4)^8
C.(-4)^2
D.(-4)^15

anonymous · Answer

This is a problem that deals with the properties of exponents. When a value that is raised to a certain power is raised to another power, they multiply. Basically,
$$(x^{a})^b=x^{ab}$$so in this problem, simply multiply the 5 and 3 to give you $$(-4)^{15}$$

imstuck · Answer

Just like before, this is equivalent to $$(-4^{5})^{3}=(-4)^{15}=-1073741824$$

anonymous · Answer

so what about this 12^21?

anonymous · Answer

That's just a huge number.$$12^{21}=4.6\times 10^{22}$$

anonymous · Answer

ah here are the available options for answers : 
A. (12)^20
B.(12^8)^-12
C.(12^7)^3
D.(12^7)^14

anonymous · Answer

Oh I see. So it's the same concept as before. Look for the 2 exponents that multiply to be 21. Looking through all the answers, C is the most logical because$$(12^{7})^3=12^{21}$$

anonymous · Answer

Wow okay thanks very much I pretty much got all the rest after that one, it really is just that easy. again thank you!

anonymous · Answer

No problem! Just make sure to know all the different properties of exponents and you'll be able to solve them a lot easier!

anonymous · Answer

http://www.mathplanet.com/education/algebra-1/exponents-and-exponential-functions/properties-of-exponents This link might help :)