Which of the following is an equivalent expression to 13 −5 ⋅13 −11 with only positive exponents, generated by applying the properties of exponents?
1/26 6
1/13 6
1/13 16
1/26 16
To simplify the expression, we apply the exponent properties.
First, let's rewrite the expression with positive exponents:
13^(-5) ⋅ 13^(-11)
We can use the product of powers property, which states that when multiplying two powers with the same base, we add their exponents. In this case, we add -5 and -11:
13^(-5 + -11)
Next, we can simplify the sum of the exponents:
13^(-5 - 11)
Since the exponents have different signs, we can use the quotient of powers property, which states that when dividing two powers with the same base but different exponents, we subtract the exponents. In this case, we subtract 11 from -5:
13^(-5 - 11)
Simplifying further:
13^(-16)
To ensure positive exponents, we can rewrite the expression as:
1/13^16
Therefore, the expression is equivalent to 1/13^16.
The correct answer is 1/13 16.
Which of the following is an equivalent expression to 14−7/9−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents?
1/9 13 ⋅14−7
14−7⋅9/13
9 13/14 7
14 7/9 13
To simplify the expression and apply the property of negative integer exponents, we can rewrite the expression as follows:
14^(-7) / 9^(-13)
The property of negative integer exponents states that a negative exponent can be rewritten as the reciprocal of the base with a positive exponent.
Therefore, we can rewrite the expression as:
1 / (14^7) * (9^13)
Thus, the equivalent expression with only positive exponents is:
1/14^7 * 9^13
The correct answer is 1/14 7 * 9 13.
Which of the following is an equivalent expression to 7 3/25−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents?
7 3⋅25 4
25 4/ 7 3
7 3/ 25 4
25 4/7 −3
To simplify the expression and apply the property of negative integer exponents, we can rewrite the expression as follows:
7^3/25^4
The property of negative integer exponents states that a negative exponent can be rewritten as the reciprocal of the base with a positive exponent.
Therefore, we can rewrite the expression as:
7^3 * (25^(-4))^-1
Next, we can apply the product of powers property, which states that when raising a power to another exponent, we multiply the exponents:
7^3 * 25^(-4 * -1)
Simplifying further:
7^3 * 25^4
Thus, the equivalent expression with only positive exponents is:
7^3 * 25^4.
The correct answer is 7 3/ 25 4.
To simplify the expression 13 - 5 * 13 - 11 and generate an equivalent expression with only positive exponents, we can use the properties of exponents.
First, we have to perform the multiplication:
5 * 13 = 65
Next, we subtract 65 from 13:
13 - 65 = -52
Finally, we rewrite the expression with positive exponents:
1 / (-52) = 1/52
Therefore, the equivalent expression to 13 - 5 * 13 - 11 with only positive exponents is 1/52.
So, the correct answer is 1/52.
To simplify the given expression using the properties of exponents, we need to understand the order of operations in algebraic expressions.
First, we need to calculate the multiplication within the expression before subtraction. Therefore, we simplify -5 ⋅ 13 as -65.
Now, the expression becomes 13 - 65 - 11.
Next, we can combine like terms by subtracting 65 from 13, resulting in -52 - 11.
Now we simplify the subtraction -52 - 11, which gives us -63.
Therefore, the equivalent expression to 13 - 5 ⋅ 13 - 11 is -63.
None of the options provided (1/26 6, 1/13 6, 1/13 16, 1/26 16) are equivalent to the given expression.