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?(1 point)
Responses
154
Start Fraction 1 over 5 superscript 4 baseline end fraction
1625
Start Fraction 1 over 625 end fraction
54
5 superscript 4 baseline
595−13
To rewrite the expression with only positive exponents, we can use the property that states a negative exponent is the same as the reciprocal of the number raised to the positive exponent.
So, 59⋅5−13 can be rewritten as 59⋅(1/5)^13.
Therefore, the equivalent expression with only positive exponents is (1/5)^13.
The answer is (2) Start Fraction 1 over 5 superscript 13 baseline end fraction.
Which property of exponents was used to generate the equivalent expression 314 from 353−9?(1 point)
Responses
only the Product Rule of Exponents
only the Product Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents
only the Property of Negative Exponents
only the Property of Negative Exponents
only the Power Rule of Exponents
To find an equivalent expression to 59⋅5−13 with positive exponents, we can use the properties of integer exponents.
First, let's simplify the expression 59. Since there are no exponents involved, 59 remains the same.
Next, let's simplify the expression 5−13. Using the property of integer exponents ( a^(-n) = 1/a^n), we can rewrite 5^(-13) as 1/5^13.
Now, we can rewrite the expression 59⋅5−13 as 59 ⋅ (1/5^13).
To multiply these expressions, we can use the property of multiplying fractions (a/b ⋅ c/d = ac/bd).
So, the equivalent expression with positive exponents is (59 ⋅ 1)/(5^13), which simplifies to 59/5^13.
Therefore, the correct answer is not provided in the options. The correct equivalent expression is 59/5^13.
To find an equivalent expression with only positive exponents, we can apply the properties of integer exponents. The expression we have is 59⋅5−13.
First, let's simplify the expression 5−13. The property of negative exponents states that a−n is equal to 1 over a raised to the power of n. Applying this property to 5−13, we have 1 over 5¹³.
Therefore, the expression becomes:
59 times 1 over 5¹³.
Now, let's simplify further by using the property that aⁿ times aᵐ is equal to a raised to the power of (n + m). In this case, 59 times 1 over 5¹³ is equivalent to 59 over 5¹³.
Therefore, the equivalent expression with only positive exponents is 59 over 5¹³.