Select the equivalent expression. ((1)/(a^(-6)*a^(3)))^((5)/(3)) a^(5) (1)/(a^(5)) (1)/(root(5)(a)) root(5)(a)

Simplify inside parentheses: We start by simplifying the expression inside the parentheses before applying the exponent. ((1)/(a^(-6)*a^(3))) simplifies to (1)/(a^(-6+3)) because when you multiply powers with the same base, you add the exponents.Simplify exponent inside parentheses: Now we simplify the exponent inside the parentheses. (1)/(a^(-6+3)) simplifies to (1)/(a^(-3)) because -6 + 3 equals -3.Apply exponent to expression: Next, we apply the exponent (5/3) to the expression (1)/(a^(-3)). ((1)/(a^(-3)))^((5)/(3)) simplifies to (1)^((5)/(3))/(a^(-3*(5/3))) because when you raise a power to a power, you multiply the exponents.Simplify exponent of a: We simplify the exponent of a. a^(-3*(5/3)) simplifies to a^(-5) because -3 times (5/3) equals -5.Simplify numerator: Now we simplify the numerator (1)^((5)/(3)). Any number to the power of any real number is that number itself, so (1)^((5)/(3)) is just 1.Final expression: We are left with the expression 1/(a^(-5)). Since 1 raised to any power is still 1, and a negative exponent means the reciprocal, we can rewrite 1/(a^(-5)) as a^(5).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Select the equivalent expression.

((1)/(a^(-6)*a^(3)))^((5)/(3))

a^(5)

(1)/(a^(5))

(1)/(root(5)(a))

root(5)(a)

Select the equivalent expression. $\newline$ $\left(\frac{1}{a^{-6} \cdot a^{3}}\right)^{\frac{5}{3}}$ $\newline$ $a^{5}$ $\newline$ $\frac{1}{a^{5}}$ $\newline$ $\frac{1}{\sqrt[5]{a}}$ $\newline$ $\sqrt[5]{a}$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(\frac{1}{a^{-6} \cdot a^{3}}\right)^{\frac{5}{3}}

\newline

a^{5}

\newline

\frac{1}{a^{5}}

\newline

\frac{1}{\sqrt[5]{a}}

\newline

\sqrt[5]{a}

Simplify inside parentheses: We start by simplifying the expression inside the parentheses before applying the exponent. $\newline$ $(1)/(a^{-6}*a^{3})$ simplifies to $(1)/(a^{-6+3})$ because when you multiply powers with the same base, you add the exponents.
Simplify exponent inside parentheses: Now we simplify the exponent inside the parentheses. $\newline$ $(1)/(a^{(-6+3)})$ simplifies to $(1)/(a^{(-3)})$ because $-6 + 3$ equals $-3$ .
Apply exponent to expression: Next, we apply the exponent $(5/3)$ to the expression $(1)/(a^{-3})$ . $((1)/(a^{-3}))^{(5)/(3)}$ simplifies to $(1)^{(5)/(3)}/(a^{-3*(5/3)})$ because when you raise a power to a power, you multiply the exponents.
Simplify exponent of a: We simplify the exponent of a. $a^{(-3*(5/3))}$ simplifies to $a^{(-5)}$ because $-3$ times $(5/3)$ equals $-5$ .
Simplify numerator: Now we simplify the numerator $(1)^{(5)/(3)}$ . Any number to the power of any real number is that number itself, so $(1)^{(5)/(3)}$ is just $1$ .
Final expression: We are left with the expression $\frac{1}{a^{-5}}$ . Since $1$ raised to any power is still $1$ , and a negative exponent means the reciprocal, we can rewrite $\frac{1}{a^{-5}}$ as $a^{5}$ .