Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $$\left( \frac { t ^ { 4 } } { t ^ { - 6 } } \right) ^ { 1 / 2 }$$
A) $t ^ { 8 }$
B) $t ^ { 5 }$
C) $t ^ { - 4 }$
D) $t ^ { - 1 }$

Question

Quizplus · Accepted Answer

When simplifying the expression $\left( \frac { t ^ { 4 } } { t ^ { - 6 } } \right) ^ { 1 / 2 }$, you first simplify the fraction inside the parentheses by adding the exponents (since dividing powers with the same base requires subtracting their exponents, and a negative exponent in the denominator is equivalent to a positive exponent in the numerator). This gives $t^{4 - (-6)} = t^{10}$. Then, applying the exponent of $1/2$ (which means taking the square root), you get $t^{10 \cdot 1/2} = t^5$.

Simplify the Expression by Using the Properties of Rational Exponents (t4t−6)1/2\left( \frac { t ^ { 4 } } { t ^ { - 6 } } \right) ^ { 1 / 2 }(t−6t4​)1/2

Simplify the Expression by Using the Properties of Rational Exponents $\left( \frac { t ^ { 4 } } { t ^ { - 6 } } \right) ^ { 1 / 2 }$