Question

Which expression is equivalent to (2^3)^-5

Answer 1

Answer:

Equivalent expression is $\frac{1}{2^{15}}$

Step-by-step explanation:

Given expression $(2^3)^{-5}$

Following law of exponent are used,

$(x^a)^b=x^{ab}\:\:and\:\:x^{-a}=\frac{1}{x^a}$

So, consider

$(2^3)^{-5}$

$=2^{3\times(-5)}$

$=2^{-15}$

$=\frac{1}{2^{15}}$

Therefore, Equivalent expression is $\frac{1}{2^{15}}$

Answer 2

$\text{Use:}\\\\(a^n)^m=a^{nm}\\\\a^{-n}=\dfrac{1}{a^n}\\\\\left(2^3\right)^{-5}=2^{3\cdot(-5)}=2^{-15}=\dfrac{1}{2^{15}}$