Select the equivalent expression. (t^(-2)*t^(7))^((3)/(20)) (1)/(root(4)(t^(3))) root(3)(t^(4)) (1)/(root(3)(t^(4))) root(4)(t^(3))

Simplify Exponents: Simplify the expression inside the parentheses by adding the exponents of t. When multiplying powers with the same base, you add the exponents. t^(-2) * t^(7) = t^(-2 + 7) = t^(5)Apply Outer Exponent: Apply the outer exponent to the simplified base. Now we have (t^(5))^((3)/(20)). When raising a power to a power, you multiply the exponents. (t^(5))^((3)/(20)) = t^(5 * (3/20)) = t^(15/20)Reduce Fraction: Simplify the exponent by reducing the fraction. The fraction 15/20 can be reduced to 3/4 by dividing both the numerator and the denominator by 5. t^(15/20) = t^(3/4)Use Radical Notation: Write the expression using radical notation. An exponent of 3/4 means the fourth root of the number raised to the third power. t^(3/4) = root(4)(t^3)

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Select the equivalent expression.

(t^(-2)*t^(7))^((3)/(20))

(1)/(root(4)(t^(3)))

root(3)(t^(4))

(1)/(root(3)(t^(4)))

root(4)(t^(3))

Select the equivalent expression. $\newline$ $\left(t^{-2} \cdot t^{7}\right)^{\frac{3}{20}}$ $\newline$ $\frac{1}{\sqrt[4]{t^{3}}}$ $\newline$ $\sqrt[3]{t^{4}}$ $\newline$ $\frac{1}{\sqrt[3]{t^{4}}}$ $\newline$ $\sqrt[4]{t^{3}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(t^{-2} \cdot t^{7}\right)^{\frac{3}{20}}

\newline

\frac{1}{\sqrt[4]{t^{3}}}

\newline

\sqrt[3]{t^{4}}

\newline

\frac{1}{\sqrt[3]{t^{4}}}

\newline

\sqrt[4]{t^{3}}

Simplify Exponents: Simplify the expression inside the parentheses by adding the exponents of $t$ . When multiplying powers with the same base, you add the exponents. $t^{-2} \times t^{7} = t^{-2 + 7} = t^{5}$
Apply Outer Exponent: Apply the outer exponent to the simplified base. $\newline$ Now we have $(t^{5})^{(\frac{3}{20})}$ . When raising a power to a power, you multiply the exponents. $\newline$ $(t^{5})^{(\frac{3}{20})} = t^{5 \times (\frac{3}{20})} = t^{\frac{15}{20}}$
Reduce Fraction: Simplify the exponent by reducing the fraction. $\newline$ The fraction $\frac{15}{20}$ can be reduced to $\frac{3}{4}$ by dividing both the numerator and the denominator by $5$ . $\newline$ $t^{\frac{15}{20}} = t^{\frac{3}{4}}$
Use Radical Notation: Write the expression using radical notation. $\newline$ An exponent of $\frac{3}{4}$ means the fourth root of the number raised to the third power. $\newline$ $t^{\frac{3}{4}} = \sqrt[4]{t^3}$