Which exponential expression is equivalent to root(6)(t) ? Choose 1 answer: (A) t^(6) (B) (1)/(t^((1)/(6))) (C) t^((1)/(6)) (D) (1)/(t^(6))

Understand Rule for Conversion: First, we need to understand that the sixth root of t can be expressed as an exponent. The general rule for converting a root to an exponent is that root(n)(a) is equivalent to a^(1/n). So, we will apply this rule to root(6)(t).Apply Rule to Given Expression: Using the rule from the first step, we can express root(6)(t) as t^(1/6). This is because the index of the root (which is 6 in this case) becomes the denominator of the exponent when the radical is converted to an exponential expression.Compare with Options: Now, we will compare the expression we found, t^(1/6), with the options given in the problem: (A) t^(6) is not correct because it represents t raised to the power of 6, not the sixth root of t. (B) (1)/(t^((1)/(6))) is not correct because it represents the reciprocal of the sixth root of t. (C) t^((1)/(6)) is correct because it represents the sixth root of t, which is what we found in our calculation. (D) (1)/(t^(6)) is not correct because it represents the reciprocal of t raised to the power of 6, not the sixth root of t.

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Which exponential expression is equivalent to
root(6)(t) ?
Choose 1 answer:
(A)
t^(6)
(B)
(1)/(t^((1)/(6)))
(C)
t^((1)/(6))
(D)
(1)/(t^(6))

Which exponential expression is equivalent to $\sqrt[6]{t}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $t^{6}$ $\newline$ (B) $\frac{1}{t^{\frac{1}{6}}}$ $\newline$ (C) $t^{\frac{1}{6}}$ $\newline$ (D) $\frac{1}{t^{6}}$

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Math Problems

Algebra 2

Simplify the product of two radical expressions having same variable

Full solution

Q. Which exponential expression is equivalent to

\sqrt[6]{t}

\newline

Choose

1

answer:

\newline

(A)

t^{6}

\newline

(B)

\frac{1}{t^{\frac{1}{6}}}

\newline

(C)

t^{\frac{1}{6}}

\newline

(D)

\frac{1}{t^{6}}

Understand Rule for Conversion: First, we need to understand that the sixth root of $t$ can be expressed as an exponent. The general rule for converting a root to an exponent is that $\sqrt[n]{a}$ is equivalent to $a^{1/n}$ . So, we will apply this rule to $\sqrt[6]{t}$ .
Apply Rule to Given Expression: Using the rule from the first step, we can express $\sqrt[6]{t}$ as $t^{\frac{1}{6}}$ . This is because the index of the root (which is $6$ in this case) becomes the denominator of the exponent when the radical is converted to an exponential expression.
Compare with Options: Now, we will compare the expression we found, $t^{1/6}$ , with the options given in the problem: $\newline$ (A) $t^{6}$ is not correct because it represents $t$ raised to the power of $6$ , not the sixth root of $t$ . $\newline$ (B) $\frac{1}{t^{1/6}}$ is not correct because it represents the reciprocal of the sixth root of $t$ . $\newline$ (C) $t^{1/6}$ is correct because it represents the sixth root of $t$ , which is what we found in our calculation. $\newline$ (D) $\frac{1}{t^{6}}$ is not correct because it represents the reciprocal of $t$ raised to the power of $6$ , not the sixth root of $t$ .