Select the equivalent expression. root(18)(a^(-6)*a^(-3)) a^(2) a^((1)/(2)) a^(-(1)/(2)) a^(-2)

Understand the problem: Understand the problem. We need to simplify the expression root(18)(a^(-6)*a^(-3)) and select the equivalent expression from the given options.Apply exponent property: Apply the property of exponents for multiplication. When multiplying two exponents with the same base, we add the exponents. a^(-6) * a^(-3) = a^(-6 + -3)Perform exponent addition: Perform the addition of exponents. a^(-6 + -3) = a^(-9)Apply root to exponent: Apply the root to the exponent. The 18th root of a^(-9) can be written as a^(-9/18).Simplify exponent fraction: Simplify the fraction in the exponent. -9/18 simplifies to -1/2. a^(-9/18) = a^(-1/2)Match with given options: Match the simplified expression with the given options. The equivalent expression is a^(-(1)/(2)).

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Select the equivalent expression.

root(18)(a^(-6)*a^(-3))

a^(2)

a^((1)/(2))

a^(-(1)/(2))

a^(-2)

Select the equivalent expression. $\newline$ $\sqrt[18]{a^{-6} \cdot a^{-3}}$ $\newline$ $a^{2}$ $\newline$ $a^{\frac{1}{2}}$ $\newline$ $a^{-\frac{1}{2}}$ $\newline$ $a^{-2}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\sqrt[18]{a^{-6} \cdot a^{-3}}

\newline

a^{2}

\newline

a^{\frac{1}{2}}

\newline

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

\newline

a^{-2}

Understand the problem: Understand the problem. $\newline$ We need to simplify the expression $\sqrt[18]{a^{-6} \cdot a^{-3}}$ and select the equivalent expression from the given options.
Apply exponent property: Apply the property of exponents for multiplication. $\newline$ When multiplying two exponents with the same base, we add the exponents. $\newline$ $a^{-6} \times a^{-3} = a^{-6 + -3}$
Perform exponent addition: Perform the addition of exponents. $a^{(-6 + -3)} = a^{-9}$
Apply root to exponent: Apply the root to the exponent. $\newline$ The $18$ th root of $a^{(-9)}$ can be written as $a^{(-9/18)}$ .
Simplify exponent fraction: Simplify the fraction in the exponent. $\newline$ $-\frac{9}{18}$ simplifies to $-\frac{1}{2}$ . $\newline$ $a^{-\frac{9}{18}} = a^{-\frac{1}{2}}$
Match with given options: Match the simplified expression with the given options. $\newline$ The equivalent expression is $a^{-(1)/(2)}$ .