Question

Which of the following is an equivalent expression to 59⋅5−13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?

Answer 1

Which property of exponents was used to generate the equivalent expression 314 from 353−9?


the Property of Negative Exponents and the Product Rule of Exponents


only the Power Rule of Exponents


only the Product Rule of Exponents


only the Property of Negative Exponents

Answer 2

We can simplify $59\cdot 5-13$ by multiplying first: \begin{align*}
59\cdot 5-13 &= 295-13\\
&=282.
\end{align*} The only exponent in the expression is $5$, and $5=5^1$, so we can write $282$ as $282\cdot 1$. Because $282=282^1$, the expression $282\cdot 1$ has positive exponents. Since $282=282^1$, the number $282$ can be expressed as $282^1$, so another equivalent expression is $282^1\cdot 1=\boxed{282^1}$.