Which expressions are equivalent to (8^3)^2/8−^5? Select all that apply.
A). 8^5/8^-5
B). 8^6/8^-5
C). 8^0
D). 8^1
E). 8^10
F). 8^11
If your question means:
( 8³ )² / 8 ⁻⁵
then
( 8³ )² = 8⁶
( 8³ )² / 8 ⁻⁵ = 8⁶ / 8 ⁻⁵
Answer B
8 ⁻⁵ = 1 / 8⁵
( 8³ )² / 8 ⁻⁵ = 8⁶ / ( 1 / 8⁵ ) = 8⁶ ∙ 8⁵ = 8¹¹
Answer F
(8^a)^b = 8^(ab)
(8^3)^2 = 8^6
8^a/8^b = 8^(a-b)
6-(-5) = 11, so I'd go with F
To find the expressions that are equivalent to (8^3)^2/8^(-5), we need to simplify the exponents and perform the division.
First, let's simplify the expression (8^3)^2. To raise a power to another power, we multiply the exponents. Therefore, (8^3)^2 can be rewritten as 8^(3*2) or 8^6.
So, the expression now becomes 8^6/8^(-5). To divide powers with the same base, we subtract the exponents. Therefore, 8^6/8^(-5) can be rewritten as 8^(6-(-5)) or 8^(6+5) which equals 8^11.
Therefore, the expressions that are equivalent to (8^3)^2/8^(-5) are:
F) 8^11