Which expression is equivalent to ((3^(4))^(-6))/(3^(-5))? 3^(-29) 3^(-19) 3^(19) 3^(-21)

Simplify numerator: Simplify the numerator ((3^(4))^(-6)). When raising a power to another power, we multiply the exponents. (3^(4))^(-6) = 3^(4 * -6) = 3^(-24)Simplify denominator: Simplify the denominator 3^(-5). The denominator is already in its simplest form, so we can leave it as 3^(-5).Divide numerator by denominator: Divide the numerator by the denominator. When dividing like bases with exponents, we subtract the exponents. 3^(-24) / 3^(-5) = 3^(-24 - (-5)) = 3^(-24 + 5) = 3^(-19)Verify final expression: Verify the final expression. The final expression is 3^(-19), which is one of the options given.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

3^(-29)

3^(-19)

3^(19)

3^(-21)

Which expression is equivalent to $\frac{\left(3^{4}\right)^{-6}}{3^{-5}} ?$ $\newline$ $3^{-29}$ $\newline$ $3^{-19}$ $\newline$ $3^{19}$ $\newline$ $3^{-21}$

View step-by-step help

Home

Math Problems

Precalculus

Operations with rational exponents

Full solution

Q. Which expression is equivalent to

\frac{\left(3^{4}\right)^{-6}}{3^{-5}} ?

\newline

3^{-29}

\newline

3^{-19}

\newline

3^{19}

\newline

3^{-21}

Simplify numerator: Simplify the numerator $((3^{4})^{(-6)})$ . When raising a power to another power, we multiply the exponents. $(3^{4})^{(-6)} = 3^{4 \cdot -6} = 3^{-24}$
Simplify denominator: Simplify the denominator $3^{-5}$ . The denominator is already in its simplest form, so we can leave it as $3^{-5}$ .
Divide numerator by denominator: Divide the numerator by the denominator. $\newline$ When dividing like bases with exponents, we subtract the exponents. $\newline$ $3^{(-24)} / 3^{(-5)} = 3^{(-24 - (-5))} = 3^{(-24 + 5)} = 3^{(-19)}$
Verify final expression: Verify the final expression. $\newline$ The final expression is $3^{(-19)}$ , which is one of the options given.