Perform the indicated operations using the laws of exponents. Express the result using positive exponents. $\left( \frac { 10 ^ { 2 } } { 10 ^ { - 9 } } \right) ^ { 3 }$
A) $10 ^ { 33 }$
B) $10 ^ { 7 }$
C) $\frac { 1 } { 10 ^ { 15 } }$
D) $\frac { 1 } { 10 ^ { 33 } }$
E) $\frac { 1 } { 10 ^ { 7 } }$

Question

Quizplus · Accepted Answer

Using the laws of exponents, we have:

$$\left(\frac{10^2}{10^{-9}}\right)^3 = \left(10^{2-(-9)}\right)^3$$

Simplifying, we get:

$$\left(10^{11}\right)^3 = 10^{33}$$

Therefore, the answer is A, $10^{33}$.

Perform the Indicated Operations Using the Laws of Exponents (10210−9)3\left( \frac { 10 ^ { 2 } } { 10 ^ { - 9 } } \right) ^ { 3 }(10−9102​)3

Perform the Indicated Operations Using the Laws of Exponents $\left( \frac { 10 ^ { 2 } } { 10 ^ { - 9 } } \right) ^ { 3 }$