Select the equivalent expression. root(14)(t^(-8)*t) t^((1)/(2)) t^(2) t^(-(1)/(2)) t^(-2)

Understand the problem: Understand the problem. We need to simplify the expression root(14)(t^(-8)*t) to find an equivalent expression.Apply properties of exponents: Apply the properties of exponents. When multiplying two powers with the same base, we add the exponents. t^(-8) * t = t^(-8 + 1) = t^(-7)Apply root to the power: Apply the root to the power. The 14th root of t^(-7) can be written as t^(-7/14). Simplify the fraction -7/14 to get the exponent. t^(-7/14) = t^(-1/2)Match with given options: Match the result with the given options. The simplified expression t^(-1/2) matches one of the given options.

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Select the equivalent expression.

root(14)(t^(-8)*t)

t^((1)/(2))

t^(2)

t^(-(1)/(2))

t^(-2)

Select the equivalent expression. $\newline$ $\sqrt[14]{t^{-8} \cdot t}$ $\newline$ $t^{\frac{1}{2}}$ $\newline$ $t^{2}$ $\newline$ $t^{-\frac{1}{2}}$ $\newline$ $t^{-2}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\sqrt[14]{t^{-8} \cdot t}

\newline

t^{\frac{1}{2}}

\newline

t^{2}

\newline

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

\newline

t^{-2}

Understand the problem: Understand the problem. $\newline$ We need to simplify the expression $\sqrt[14]{t^{-8} \cdot t}$ to find an equivalent expression.
Apply properties of exponents: Apply the properties of exponents. $\newline$ When multiplying two powers with the same base, we add the exponents. $\newline$ $t^{-8} \times t = t^{-8 + 1} = t^{-7}$
Apply root to the power: Apply the root to the power. $\newline$ The $14^{\text{th}}$ root of $t^{(-7)}$ can be written as $t^{(-\frac{7}{14})}$ . $\newline$ Simplify the fraction $-\frac{7}{14}$ to get the exponent. $\newline$ $t^{(-\frac{7}{14})} = t^{(-\frac{1}{2})}$
Match with given options: Match the result with the given options. $\newline$ The simplified expression $t^{(-1/2)}$ matches one of the given options.