Select the equivalent expression. ((t^(6))/(t^(-2)))^((1)/(14)) (1)/(root(4)(t^(7))) (1)/(root(7)(t^(4))) root(7)(t^(4)) root(4)(t^(7))

Simplify Exponents in Parentheses: Simplify the expression inside the parentheses by adding the exponents of t. When dividing powers with the same base, subtract the exponents: t^(a) / t^(b) = t^(a-b). So, (t^(6)) / (t^(-2)) = t^(6 - (-2)) = t^(6 + 2) = t^(8).Apply Exponent Rule: Apply the exponent (1/14) to the simplified base t^(8). Now we have (t^(8))^((1)/(14)). When raising a power to a power, multiply the exponents: (t^(a))^b = t^(a*b). So, (t^(8))^((1)/(14)) = t^(8*(1/14)) = t^(8/14) = t^(4/7).Convert to Radical Expression: Convert the exponent to a radical expression. The expression t^(4/7) can be written as the 7th root of t raised to the 4th power, which is root(7)(t^(4)).

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Select the equivalent expression.

((t^(6))/(t^(-2)))^((1)/(14))

(1)/(root(4)(t^(7)))

(1)/(root(7)(t^(4)))

root(7)(t^(4))

root(4)(t^(7))

Select the equivalent expression. $\newline$ $\left(\frac{t^{6}}{t^{-2}}\right)^{\frac{1}{14}}$ $\newline$ $\frac{1}{\sqrt[4]{t^{7}}}$ $\newline$ $\frac{1}{\sqrt[7]{t^{4}}}$ $\newline$ $\sqrt[7]{t^{4}}$ $\newline$ $\sqrt[4]{t^{7}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(\frac{t^{6}}{t^{-2}}\right)^{\frac{1}{14}}

\newline

\frac{1}{\sqrt[4]{t^{7}}}

\newline

\frac{1}{\sqrt[7]{t^{4}}}

\newline

\sqrt[7]{t^{4}}

\newline

\sqrt[4]{t^{7}}

Simplify Exponents in Parentheses: Simplify the expression inside the parentheses by adding the exponents of $t$ . When dividing powers with the same base, subtract the exponents: $t^{a} / t^{b} = t^{a-b}$ . So, $(t^{6}) / (t^{-2}) = t^{6 - (-2)} = t^{6 + 2} = t^{8}.$
Apply Exponent Rule: Apply the exponent $(1/14)$ to the simplified base $t^{8}$ . Now we have $(t^{8})^{(1)/(14)}$ . When raising a power to a power, multiply the exponents: $(t^{a})^{b} = t^{a*b}$ . So, $(t^{8})^{(1)/(14)} = t^{8*(1/14)} = t^{8/14} = t^{4/7}$ .
Convert to Radical Expression: Convert the exponent to a radical expression. $\newline$ The expression $t^{\frac{4}{7}}$ can be written as the $7$ th root of $t$ raised to the $4$ th power, which is $\sqrt[7]{t^4}$ .