Simplify Expressions Using the Properties for Exponents.

$$\begin{gathered} \left(a\right)r^{-3} \\ \left(b\right){10}^{-5} \\ \left(c\right)\frac{1}{q^{-10}} \\ \left(d\right)\frac{1}{{10}^{-3}} \end{gathered}$$

Properties of Negative Exponents : If $n$ is an integer and $a\ne 0$, then$a^{-n}=\frac{1}{a^n}or\frac{1}{a^n}=a^n$.

Use the definition of a negative exponent $a^{-n}=\frac{1}{a^n}$, to simplify the given expression.

$r^{-3}=\frac{1}{r^3}$.

Properties of Negative Exponents : If$n$is an integer and$a\ne 0$, then$a^{-n}=\frac{1}{a^n}or\frac{1}{a^n}=a^n$.

Use the definition of a negative exponent $a^{-n}=\frac{1}{a^n}$, to simplify the given expression.

$$\begin{gathered} {10}^{-5}=\frac{1}{{10}^5} \\ {10}^{-5}=\frac{1}{100,000} \end{gathered}$$

Properties of Negative Exponents : If$n$is an integer and $a\ne 0$, then$a^{-n}=\frac{1}{a^n}or\frac{1}{a^n}=a^n$.

Use the definition of a negative exponent $\frac{1}{a^{-n}}=a^n$, to simplify the given expression.

$\frac{1}{q^{-10}}=q^{10}$.

Properties of Negative Exponents : If $n$is an integer and $a\ne 0$, then$a^{-n}=\frac{1}{a^n}or\frac{1}{a^n}=a^n$.

Use the definition of a negative exponent $\frac{1}{a^{-n}}=a^n$, to simplify the given expression.

$$\begin{gathered} \frac{1}{{10}^{-3}}={10}^3 \\ \frac{1}{{10}^{-3}}=1,000 \end{gathered}$$