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

Simplify Exponent: Simplify the expression (2^-6)^1. When an exponent is raised to another exponent, we multiply the exponents. In this case, the exponent 1 does not change the value of the base or its exponent, so (2^-6)^1 simplifies to 2^-6. Calculation: (2^-6)^1 = 2^(-6*1) = 2^-6Calculate Simplified Expression: Compare the simplified expression to the choices given. We have determined that (2^-6)^1 simplifies to 2^-6. Now we need to compare this to the choices given to see which ones are equivalent. (A) 2^-5 is not equivalent because the exponent -5 is not the same as -6. (B) 1/2^6 is equivalent because 2^-6 can be written as 1/2^6. (C) 1/2^-5 is not equivalent because the negative exponent in the denominator implies a positive exponent in the numerator, which is not the same as 2^-6. (D) 2^-6 is equivalent because it is the same expression we started with.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

Home

Math Problems

Algebra 1

Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

(2^{-6})^1

\newline

Multi-select Choices:

\newline

(A)

2^{-5}

\newline

(B)

\frac{1}{2^6}

\newline

(C)

\frac{1}{2^{-5}}

\newline

(D)

2^{-6}

Simplify Exponent: Simplify the expression $(2^{-6})^1$ . When an exponent is raised to another exponent, we multiply the exponents. In this case, the exponent $1$ does not change the value of the base or its exponent, so $(2^{-6})^1$ simplifies to $2^{-6}$ . Calculation: $(2^{-6})^1 = 2^{(-6*1)} = 2^{-6}$
Calculate Simplified Expression: Compare the simplified expression to the choices given. $\newline$ We have determined that $(2^{-6})^1$ simplifies to $2^{-6}$ . Now we need to compare this to the choices given to see which ones are equivalent. $\newline$ (A) $2^{-5}$ is not equivalent because the exponent $-5$ is not the same as $-6$ . $\newline$ (B) $\frac{1}{2^6}$ is equivalent because $2^{-6}$ can be written as $\frac{1}{2^6}$ . $\newline$ (C) $\frac{1}{2^{-5}}$ is not equivalent because the negative exponent in the denominator implies a positive exponent in the numerator, which is not the same as $2^{-6}$ . $\newline$ (D) $2^{-6}$ is equivalent because it is the same expression we started with.