Select all the expressions that are equivalent to 6^5/3^5. Multi-select Choices: (A)1/2^5 (B)1/2^-5 (C)2 (D)2^0

Question

Select all the expressions that are equivalent to 6^5/3^5.   Multi-select Choices: (A)1/2^5 (B)1/2^-5 (C)2 (D)2^0

Bytelearn · Accepted Answer

Simplify Expression: Simplify the given expression using the properties of exponents. We know that (a^m)/(a^n) = a^(m-n) when a is not equal to 0. Here, we can apply this property to the expression 6^5/3^5 by considering 6 as 2*3. So, (6^5)/(3^5) = ((2*3)^5)/(3^5) = (2^5 * 3^5)/(3^5). Now, we can cancel out the common factor of 3^5 from the numerator and the denominator.Apply Property: After canceling out the common factor, we are left with 2^5. So, (6^5)/(3^5) simplifies to 2^5. Now, let's compare this result with the given choices.Cancel Common Factor: Check each choice to see if it is equivalent to 2^5. (A) 1/2^5 is not equivalent to 2^5 because 1/2^5 is the reciprocal of 2^5.Final Simplification: Check choice (B). (B) 1/2^-5 is equivalent to 2^5 because the negative exponent means that the base (2) is on the other side of the fraction line. So, 1/2^-5 is the same as 2^5.Check Choice (A): Check choice (C). (C) 2 is not equivalent to 2^5 because 2 is the same as 2^1, and 2^1 is not equal to 2^5.Check Choice (B): Check choice (D). (D) 2^0 is not equivalent to 2^5 because any non-zero number raised to the power of 0 is 1, so 2^0 is 1, which is not equal to 2^5.

Select all the expressions that are equivalent to $\frac{6^5}{3^5}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{2^5}$ $\newline$ (B) $\frac{1}{2^{-5}}$ $\newline$ (C) $2$ $\newline$ (D) $2^0$

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Select all the expressions that are equivalent to $\frac{6^5}{3^5}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{2^5}$ $\newline$ (B) $\frac{1}{2^{-5}}$ $\newline$ (C) $2$ $\newline$ (D) $2^0$