Which expression is equivalent to (2^(-5))/(2^(-3))×2^(-4) ? 2^(2) 2^(-6) 2^(-7) 2^(-2)

Identify Properties: Identify the properties of exponents that will be used to simplify the expression. When dividing like bases with exponents, subtract the exponents: a^m / a^n = a^(m-n). When multiplying like bases with exponents, add the exponents: a^m * a^n = a^(m+n).Apply Division Property: Apply the division property to (2^(-5))/(2^(-3)). Subtract the exponents: -5 - (-3) = -5 + 3 = -2. So, (2^(-5))/(2^(-3)) simplifies to 2^(-2).Multiply Result: Now multiply the result, 2^(-2), by 2^(-4) using the multiplication property of exponents. Add the exponents: -2 + (-4) = -2 - 4 = -6. So, 2^(-2) * 2^(-4) simplifies to 2^(-6).Check Final Result: Check the final result to ensure no mathematical errors were made. The properties of exponents have been correctly applied, and the calculations are correct.

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Q. Which expression is equivalent to

\frac{2^{-5}}{2^{-3}} \times 2^{-4}

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2^{2}

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2^{-6}

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2^{-7}

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2^{-2}

Identify Properties: Identify the properties of exponents that will be used to simplify the expression. When dividing like bases with exponents, subtract the exponents: $a^m / a^n = a^{(m-n)}$ . When multiplying like bases with exponents, add the exponents: $a^m \times a^n = a^{(m+n)}$ .
Apply Division Property: Apply the division property to $(2^{-5})/(2^{-3})$ . Subtract the exponents: $-5 - (-3) = -5 + 3 = -2$ . $\newline$ So, $(2^{-5})/(2^{-3})$ simplifies to $2^{-2}$ .
Multiply Result: Now multiply the result, $2^{-2}$ , by $2^{-4}$ using the multiplication property of exponents. Add the exponents: $-2 + (-4) = -2 - 4 = -6$ . So, $2^{-2} \times 2^{-4}$ simplifies to $2^{-6}$ .
Check Final Result: Check the final result to ensure no mathematical errors were made. The properties of exponents have been correctly applied, and the calculations are correct.