Which expression is equivalent to ((2^(6))/(2^(0)))^(-1) ? 2^(-6) 2^(5) 2^(-7) 0

Simplify Base: Simplify the base before applying the negative exponent. We have the expression ((2^(6))/(2^(0)))^(-1). First, we need to simplify the base. Since any number to the power of 0 is 1, we have 2^(0) = 1. So the expression simplifies to (2^(6)/1)^(-1), which is just 2^(6)^(-1).Apply Rule: Apply the negative exponent rule. The negative exponent rule states that a^(-n) = 1/(a^n). Applying this rule to our expression, we get 1/(2^(6)).Rewrite with Negative Exponent: Rewrite the expression with a negative exponent. Instead of writing the expression as a fraction, we can write it with a negative exponent: 2^(-6).Check Answer Choices: Check the answer choices. We need to find the expression that is equivalent to our result. The correct answer is 2^(-6).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which expression is equivalent to
((2^(6))/(2^(0)))^(-1) ?

2^(-6)

2^(5)

2^(-7)
0

Which expression is equivalent to $\left(\frac{2^{6}}{2^{0}}\right)^{-1}$ ? $\newline$ $2^{-6}$ $\newline$ $2^{5}$ $\newline$ $2^{-7}$ $\newline$ $0$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Which expression is equivalent to

\left(\frac{2^{6}}{2^{0}}\right)^{-1}

\newline

2^{-6}

\newline

2^{5}

\newline

2^{-7}

\newline

0

Simplify Base: Simplify the base before applying the negative exponent. $\newline$ We have the expression $((2^{6})/(2^{0}))^{-1}$ . First, we need to simplify the base. Since any number to the power of $0$ is $1$ , we have $2^{0} = 1$ . So the expression simplifies to $(2^{6}/1)^{-1}$ , which is just 2^{6}^{-1}.
Apply Rule: Apply the negative exponent rule. $\newline$ The negative exponent rule states that $a^{-n} = \frac{1}{a^n}$ . Applying this rule to our expression, we get $\frac{1}{2^{6}}$ .
Rewrite with Negative Exponent: Rewrite the expression with a negative exponent. $\newline$ Instead of writing the expression as a fraction, we can write it with a negative exponent: $2^{-6}$ .
Check Answer Choices: Check the answer choices. $\newline$ We need to find the expression that is equivalent to our result. The correct answer is $2^{-6}$ .