Perform the indicated operations using the laws of exponents. Express the result using positive exponents. $\left( \frac { 10 ^ { - 4 } } { 10 ^ { - 7 } } \right) ^ { 3 }$
A) $\frac { 1 } { 10 ^ { 9 } }$
B) $10 ^ { 27 }$
C) $\frac { 1 } { 10 ^ { 5 } }$
D) $10 ^ { 9 }$
E) $\frac { 1 } { 10 ^ { 27 } }$

Question

Quizplus · Accepted Answer

When dividing powers with the same base, subtract the exponents: $10^{-4} / 10^{-7} = 10^{(-4)-(-7)} = 10^{3}$. Raising this to the 3rd power: $(10^{3})^{3} = 10^{3*3} = 10^{9}$.

Perform the Indicated Operations Using the Laws of Exponents (10−410−7)3\left( \frac { 10 ^ { - 4 } } { 10 ^ { - 7 } } \right) ^ { 3 }(10−710−4​)3

Perform the Indicated Operations Using the Laws of Exponents $\left( \frac { 10 ^ { - 4 } } { 10 ^ { - 7 } } \right) ^ { 3 }$