Which values are equivalent to (2[2]⋅2[−4])[3]÷(2[−3])? (Select ALL that apply.) (If it's in brackets, it's an exponent.) A) -8 B) -6 C) 2[-3] D) -1/8 E) 1/8 F) 2[3] G) 6 H) 8
Mathematics · High School · Thu Feb 04 2021
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*note:- here digits in bracket are exponent or power.
- Law of Product: a^m × a^n = a^m+n
- Law of Quotient: a^m/a^n = a^m-n
- Law of Negative Exponent: a^-m = 1/a^m
- Law of Power of a Power: (a^m)^n = a^mn
- Law of Power of a Quotient: (a/b)^m = a^m/b^m
Given Expression :- (2[2].2[-4])[3]/2[-3] its equivalent value is:-
we can write it as (2^2 * 2^-4)^3/ 2^-3 (apply law of product)
= (2^2+(-4))^3 / 2^-3
=(2^-2)^3 */2^-3 (apply law of power of power)
= 2^-6 /2^-3 (apply law of product)
=2^(-6-(-3)) (apply law of quotient)
=2^(-6+3)
=2^-3 (apply law of negative Exponent)
=1/ 2^3
=1/8 (Answer)