Which expression is equivalent to (6^(-2))/((6^(0))^(-1))? (1)/(36) 36 0 1

Simplify Denominator: Simplify the denominator. The expression in the denominator is (6^(0))^(-1). Since any number raised to the power of 0 is 1, we have 6^(0) = 1. Therefore, (6^(0))^(-1) is the same as 1^(-1).Simplify 1^(-1): Simplify 1^(-1). Any number raised to the power of -1 is the reciprocal of that number. Since 1 is the number in question, its reciprocal is also 1. Therefore, 1^(-1) = 1.Rewrite Expression: Rewrite the original expression with the simplified denominator. Now that we have simplified the denominator to 1, the original expression (6^(-2))/((6^(0))^(-1)) becomes 6^(-2)/1.Simplify Expression: Simplify the expression 6^(-2)/1. Since dividing by 1 does not change the value of the numerator, 6^(-2)/1 is simply 6^(-2). A negative exponent indicates the reciprocal of the base raised to the positive of that exponent. Therefore, 6^(-2) is equivalent to 1/(6^2).Calculate 6^2: Calculate 6^2. 6^2 means 6 multiplied by itself, which is 36. So, 1/(6^2) is 1/36.Identify Equivalent Expression: Identify the equivalent expression. The equivalent expression to the original problem (6^(-2))/((6^(0))^(-1)) is 1/36.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

(1)/(36)
36
0
1

Which expression is equivalent to $\frac{6^{-2}}{\left(6^{0}\right)^{-1}} ?$ $\newline$ $\frac{1}{36}$ $\newline$ $36$ $\newline$ $0$ $\newline$ $1$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Which expression is equivalent to

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

\newline

\frac{1}{36}

\newline

36

\newline

0

\newline

1

Simplify Denominator: Simplify the denominator. $\newline$ The expression in the denominator is $(6^{0})^{(-1)}$ . Since any number raised to the power of $0$ is $1$ , we have $6^{0} = 1$ . Therefore, $(6^{0})^{(-1)}$ is the same as $1^{(-1)}$ .
Simplify $1^{-1}$ : Simplify $1^{-1}$ . Any number raised to the power of $-1$ is the reciprocal of that number. Since $1$ is the number in question, its reciprocal is also $1$ . Therefore, $1^{-1} = 1$ .
Rewrite Expression: Rewrite the original expression with the simplified denominator. $\newline$ Now that we have simplified the denominator to $1$ , the original expression $(6^{-2})/((6^{0})^{-1})$ becomes $6^{-2}/1$ .
Simplify Expression: Simplify the expression $6^{-2}/1$ . Since dividing by $1$ does not change the value of the numerator, $6^{-2}/1$ is simply $6^{-2}$ . A negative exponent indicates the reciprocal of the base raised to the positive of that exponent. Therefore, $6^{-2}$ is equivalent to $1/(6^2)$ .
Calculate $6^2$ : Calculate $6^2$ . $\newline$ $6^2$ means $6$ multiplied by itself, which is $36$ . So, $1/(6^2)$ is $1/36$ .
Identify Equivalent Expression: Identify the equivalent expression. $\newline$ The equivalent expression to the original problem $\frac{6^{-2}}{(6^{0})^{-1}}$ is $\frac{1}{36}$ .