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?
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 $282^1\cdot 1=\boxed{282^1}$.
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
To generate an equivalent expression with only positive exponents, we can utilize the properties of integer exponents.
The expression we are given is 59⋅5^(-13).
To convert 5^(-13) to a positive exponent, we can use the property that a negative exponent is the reciprocal of the positive exponent. Therefore, 5^(-13) can be rewritten as 1/5^13.
Now we can substitute this back into the original expression:
59⋅5^(-13) = 59⋅(1/5^13)
To simplify further, we can combine 59 with 1/5^13 by multiplying the numerators and the denominators:
59⋅(1/5^13) = (59⋅1)/(5^13)
Thus, an equivalent expression with only positive exponents, generated by applying the properties of integer exponents, is (59⋅1)/(5^13).
To find an equivalent expression to 59⋅5−13 with only positive exponents, we can use the properties of integer exponents. Let's break down the steps to simplify the expression:
Step 1: Rewrite 59 as 5^9.
The expression now becomes 5^9⋅5−13.
Step 2: Apply the property of multiplication with exponents.
When multiplying two terms with the same base, we add their exponents. So, we add 9 and -13:
5^9+(-13).
Step 3: Simplify the exponent.
To simplify the exponent, we subtract -13 from 9:
5^9+(-13) = 5^-4.
So, an equivalent expression to 59⋅5−13 with only positive exponents, generated by applying the properties of integer exponents, is 5^-4.