Apply the Properties of Integer Exponents to generate equivalent expressions to (143⋅27−7)034 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
thats incorrect, do you have a different answer?
I apologize for the incorrect response. Let's try again:
To apply the properties of integer exponents and generate equivalent expressions with positive exponents, we can use the following rules:
1) Product Rule: (ab)^n = a^n * b^n
2) Power Rule: (a^n)^m = a^(n*m)
3) Negative Exponent Rule: a^(-n) = 1/a^n
4) Zero Exponent Rule: a^0 = 1
Let's apply these rules to the expression (143⋅27−7)034:
(143⋅27−7)034
= (143^0 * (27^(-7)))^34 (Using the zero exponent rule and negative exponent rule)
= 1^34 * (1/(27^7))^34
= 1 * (1^34/(27^7)^34) (Using the power rule)
= 1/(27^(7*34)) (Simplifying the exponents)
= 1/27^238
Therefore, the equivalent expression with positive exponents is 1/27^238.
The answer is 1/27^238, which is a simplified fraction with no remaining exponents.
Apply the Properties of Integer Exponents to generate equivalent expressions to (43 ⋅ 7−2)−579 ⋅ 4−13 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
To apply the properties of integer exponents and generate equivalent expressions with positive exponents, we can use the following rules:
1) Product Rule: (ab)^n = a^n * b^n
2) Power Rule: (a^n)^m = a^(n*m)
3) Negative Exponent Rule: a^(-n) = 1/a^n
4) Zero Exponent Rule: a^0 = 1
Let's apply these rules to the expression (43 ⋅ 7^(-2))^(-579) ⋅ 4^(-13):
(43 ⋅ 7^(-2))^(-579) ⋅ 4^(-13)
= (43^(-579) ⋅ (7^(-2))^(-579)) ⋅ (4^(-13))
= (43^(-579) ⋅ 7^(2*(-579))) ⋅ 4^(-13) (Applying the negative exponent rule)
= (43^(-579) ⋅ 7^(-1158)) ⋅ 4^(-13)
Now, let's simplify the exponents:
= (1/43^579) ⋅ (1/7^1158) ⋅ (1/4^13) (Applying the negative exponent rule)
= 1/(43^579 ⋅ 7^1158 ⋅ 4^13)
So, the equivalent expression with positive exponents is 1/(43^579 ⋅ 7^1158 ⋅ 4^13).
This expression cannot be simplified further.
can you simplify it shorter?
Apologies for the confusion. Let's simplify the expression further:
Using the rule (a^m)^n = a^(m * n), we can simplify the exponents:
(43^(-579) ⋅ 7^(-1158)) ⋅ 4^(-13)
= (1 / 43^579) ⋅ (1 / 7^1158) ⋅ (1 / 4^13)
Using the rule (a / b)^n = a^n / b^n, we can combine the fractions:
= 1 / (43^579 ⋅ 7^1158 ⋅ 4^13)
Now, using the commutative property of multiplication, we can rearrange the terms:
= 1 / (43^579 ⋅ 4^13 ⋅ 7^1158)
Finally, using the associative property of multiplication, we can group the terms together:
= 1 / [(43 ⋅ 4)^13 ⋅ 7^1158]
= 1 / (172^13 ⋅ 7^1158)
Therefore, the simplified fraction with no remaining exponents is 1 / (172^13 ⋅ 7^1158).
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
1/5^4
Start Fraction 1 over 5 superscript 4 baseline end fraction
5^9/5^−13
Start Fraction 5 superscript 9 baseline over 5 superscript negative 13 baseline End Fraction
1/625
Start Fraction 1 over 625 end fraction
5^4
To generate an equivalent expression to 59⋅5^−13 with only positive exponents, we can apply the properties of integer exponents.
Let's use the negative exponent rule, which states that a^(-n) = 1/a^n.
59⋅5^−13 = 59/(5^13)
Therefore, the equivalent expression with positive exponents is 59/(5^13).
Out of the given responses, the equivalent expression that matches this form is:
5^9/5^−13 -> This is equivalent to 5^9 * 5^13 = 5^(9+13) = 5^22
Hence, the correct equivalent expression is 5^22.
Which of the following is an equivalent expression to 5^9⋅5^−13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
1/5^4
Start Fraction 1 over 5 superscript 4 baseline end fraction
5^9/5^−13
Start Fraction 5 superscript 9 baseline over 5 superscript negative 13 baseline End Fraction
1/625
Start Fraction 1 over 625 end fraction
5^4
To find the equivalent expression to 5^9⋅5^−13 with only positive exponents, we can use the properties of integer exponents.
The rule we can apply here is the product rule, which states that a^m * a^n = a^(m+n).
Therefore, for 5^9⋅5^−13, we can combine the exponents:
5^9⋅5^−13 = 5^(9+(-13))
Simplifying the exponent, we get:
5^(9+(-13)) = 5^(-4)
So, the equivalent expression with positive exponents is 5^(-4).
Out of the given responses, the equivalent expression that matches this form is:
1/5^4
Hence, the correct equivalent expression is 1/5^4.