Select all the expressions that are equivalent to 2^-1 * 2^-4. Multi-select Choices: (A)1/2^-5 (B)1/2^5 (C)2^-5 (D)2^4

Question

Select all the expressions that are equivalent to 2^-1 * 2^-4.   Multi-select Choices: (A)1/2^-5 (B)1/2^5 (C)2^-5 (D)2^4

Bytelearn · Accepted Answer

Simplify Exponents: Simplify the expression 2^-1 * 2^-4 by adding the exponents. When multiplying powers with the same base, we add the exponents. 2^-1 * 2^-4 = 2^(-1 + -4) = 2^-5Compare Simplified Expression: Compare the simplified expression to the choices given. We have simplified the expression to 2^-5. Now we need to determine which of the given choices are equivalent to this expression.Evaluate Choice (A): Evaluate choice (A) 1/2^-5. The expression 1/2^-5 is equivalent to 2^5 because a negative exponent indicates that the base should be on the other side of the fraction line. 1/2^-5 = 2^5 This is not equivalent to 2^-5.Evaluate Choice (B): Evaluate choice (B) 1/2^5. The expression 1/2^5 is the reciprocal of 2^5, which is equivalent to 2^-5. 1/2^5 = 2^-5 This is equivalent to 2^-5.Evaluate Choice (C): Evaluate choice (C) 2^-5. The expression 2^-5 is exactly the same as our simplified expression. 2^-5 = 2^-5 This is equivalent to 2^-5.Evaluate Choice (D): Evaluate choice (D) 2^4. The expression 2^4 is the reciprocal of 2^-4, which is not equivalent to 2^-5. 2^4 ≠ 2^-5 This is not equivalent to 2^-5.

Select all the expressions that are equivalent to $2^{-1} \times 2^{-4}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{2^{-5}}$ $\newline$ (B) $\frac{1}{2^{5}}$ $\newline$ (C) $2^{-5}$ $\newline$ (D) $2^{4}$

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Select all the expressions that are equivalent to 2−1×2−42^{-1} \times 2^{-4}2−1×2−4.\newlineMulti-select Choices:\newline(A)12−5\frac{1}{2^{-5}}2−51​\newline(B)125\frac{1}{2^{5}}251​\newline(C)2−52^{-5}2−5\newline(D)242^{4}24

Select all the expressions that are equivalent to $2^{-1} \times 2^{-4}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{2^{-5}}$ $\newline$ (B) $\frac{1}{2^{5}}$ $\newline$ (C) $2^{-5}$ $\newline$ (D) $2^{4}$