Which exponential expression is equivalent to (root(3)(t))^(2) ? Choose 1 answer: (A) (t^(3))/(t^(2)) (B) (t^(2))/(t^(3)) (c) t^((3)/(2)) (D) t^((2)/(3))

Express Cube Root in Exponential Form: We need to express the cube root of t squared in exponential form. The cube root of t can be written as t raised to the power of 1/3. Therefore, (root(3)(t)) can be written as t^(1/3).Apply Power of a Power Rule: Now we need to apply the power of a power rule, which states that (a^(m))^n = a^(m*n). In this case, we have (t^(1/3))^2, which means we multiply the exponents: 1/3 * 2.Multiply Exponents: Multiplying the exponents gives us t^(1/3 * 2) = t^(2/3). This is the simplified exponential form of the original expression.Compare with Choices: Comparing our result with the given choices, we find that t^(2/3) matches choice (D).

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Which exponential expression is equivalent to
(root(3)(t))^(2) ?
Choose 1 answer:
(A)
(t^(3))/(t^(2))
(B)
(t^(2))/(t^(3))
(c)
t^((3)/(2))
(D)
t^((2)/(3))

Which exponential expression is equivalent to $(\sqrt[3]{t})^{2}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{t^{3}}{t^{2}}$ $\newline$ (B) $\frac{t^{2}}{t^{3}}$ $\newline$ (C) $t^{\frac{3}{2}}$ $\newline$ (D) $t^{\frac{2}{3}}$

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Math Problems

Grade 7

Identify equivalent linear expressions I

Full solution

Q. Which exponential expression is equivalent to

(\sqrt[3]{t})^{2}

\newline

Choose

1

answer:

\newline

(A)

\frac{t^{3}}{t^{2}}

\newline

(B)

\frac{t^{2}}{t^{3}}

\newline

(C)

t^{\frac{3}{2}}

\newline

(D)

t^{\frac{2}{3}}

Express Cube Root in Exponential Form: We need to express the cube root of $t^2$ in exponential form. The cube root of $t$ can be written as $t$ raised to the power of $\frac{1}{3}$ . Therefore, $\sqrt[3]{t}$ can be written as $t^{\frac{1}{3}}$ .
Apply Power of a Power Rule: Now we need to apply the power of a power rule, which states that $(a^{m})^{n} = a^{m*n}$ . In this case, we have $(t^{\frac{1}{3}})^{2}$ , which means we multiply the exponents: $\frac{1}{3} * 2$ .
Multiply Exponents: Multiplying the exponents gives us $t^{(1/3 \cdot 2)} = t^{2/3}$ . This is the simplified exponential form of the original expression.
Compare with Choices: Comparing our result with the given choices, we find that $t^{\frac{2}{3}}$ matches choice $(D)$ .