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
5⁹/5 - ¹²
1/5⁴
5⁴
1/625
The correct answer is 1/625.
To simplify the expression 5⁹ • 5 - ¹³, we can use the property of exponents which states that when multiplying two numbers with the same base, you add the exponents. Thus, 5⁹ • 5 - ¹³ simplifies to 5⁹ + (-13).
To make the exponents positive, we can rewrite the expression as 5⁹ ÷ 5¹³.
Note: Let's clarify that 5⁹/5 - ¹² is not equivalent to the original expression.
Which property of exponents was used to generate the equivalent expression 3¹⁴ from 3⁵/3 - ⁹ ?
Only the power rule of exponents
Only the property of negative 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 were used to generate the equivalent expression 3¹⁴ from 3⁵/3 - ⁹.
To simplify the expression 3⁵/3 - ⁹, we can apply the property of negative exponents, which states that a number with a negative exponent is equal to the reciprocal of the number with the same base and positive exponent. Thus, 3⁵/3 - ⁹ simplifies to (3⁵ • 3⁻⁹).
Next, we can apply the product rule of exponents, which states that when multiplying two numbers with the same base, you add the exponents. Thus, (3⁵ • 3⁻⁹) simplifies to 3⁵ + (-9), which is equivalent to 3¹⁴.
What is the answer
Only the power rule of exponents
Only the property of negative exponents
Only the product rule of exponents
The property of negative exponents and the product rule of exponents
The correct answer is "Only the property of negative exponents and the product rule of exponents."
This is because the original expression, 3⁵/3 - ⁹, can be simplified using both the property of negative exponents, where a number with a negative exponent is equal to the reciprocal of the number with the same base and positive exponent, and the product rule of exponents, which states that when multiplying two numbers with the same base, you add the exponents.
Which of the following is an equivalent expression to 15⁰ • 7 - ²/ (-4) - ³ with only positive exponents that has been generated by applying the properties of integer exponents
4³/7²
(- 4)³/7²
7²/(- 4)²
1/7² • (- 4)-³
The answer is 1/7² • (- 4)-³.
To simplify the expression 15⁰ • 7 - ² / (-4) - ³, we can use the property of an exponent raised to the power of 0, which states that any number (except 0) raised to the power of 0 equals 1. Thus, 15⁰ simplifies to 1.
Next, we can apply the property of negative exponents, which states that a number with a negative exponent is equal to the reciprocal of the number with the same base and positive exponent. Therefore, 7 - ² simplifies to 1/7².
Finally, we can further simplify the expression as 1/7² • (-4) - ³, applying the property of multiplying numbers with the same base and different exponents. Since (-4) - ³ = (-4)³, the final simplified expression is 1/7² • (-4)³.
Which of the following is the equivalent expression to (15-³ • 4⁷)⁰/4-³ that has been generated by applying the properties of integer exponents
1/64
60/4-³
1 • 4-³
64
The equivalent expression is 1.
To simplify the expression (15-³ • 4⁷)⁰/4-³, we can first apply the property of negative exponents, which states that a number with a negative exponent is equal to the reciprocal of the number with the same base and positive exponent. Thus, 15-³ simplifies to 1/15³.
Next, we can simplify 4⁷ as 4⁷, as 4⁷ already has a positive exponent.
Now we have (1/15³ • 4⁷)⁰/4-³. According to the order of operations, we should resolve the parentheses first. (1/15³ • 4⁷)⁰ becomes 1/15³ • 4⁷⁰.
Next, we apply the property of any non-zero number raised to the power of 0, which states that any non-zero number raised to the power of 0 equals 1. Thus, 4⁷⁰ simplifies to 1.
Finally, we have 1/15³ • 1/4-³. Applying the property of dividing two numbers with the same base, we subtract the exponents. 1/4-³ simplifies to 4³, which is equal to 64.
So, the final expression is 1/15³ • 64, which is equivalent to 1.
To find an equivalent expression with only positive exponents, we can apply the properties of integer exponents.
The expression given is 5⁹ • 5 - ¹³.
The first property we can use is that when we multiply two numbers with the same base, we add their exponents. So, 5⁹ • 5 - ¹³ can be written as 5^(9 + (-13)).
Now, we need to simplify the exponent. When we add a positive number and a negative number, we subtract the smaller magnitude from the larger magnitude and keep the sign of the larger magnitude. So, 9 + (-13) becomes 9 - 13 = -4.
Therefore, the expression 5⁹ • 5 - ¹³ is equivalent to 5^(-4).
To convert this to a positive exponent, we can use the property that a negative exponent is equal to the reciprocal of the positive exponent. So, 5^(-4) can be written as 1/5⁴.
Therefore, the equivalent expression with only positive exponents is 1/5⁴.