To generate equivalent expressions with only positive exponents, we can apply the properties of integer exponents.
First, let's simplify the expression inside the parentheses:
14^3 * 27^(-7)
Using the property (a^m)^n = a^(m*n), we can rewrite this as:
(14^3) * (27^(-7))
Now, let's calculate the values of 14^3 and 27^(-7):
14^3 = 14 * 14 * 14 = 2744
27^(-7) = 1 / (27^7) ≈ 8.621 x 10^(-8) (approximate value)
Now, our expression becomes:
(2744) * (8.621 x 10^(-8))
Next, let's rewrite 3^4:
3^4 = 3 * 3 * 3 * 3 = 81
Now, our expression becomes:
(2744) * (8.621 x 10^(-8)) / (81)
Finally, let's raise this expression to the power of (0/3) using the property a^0 = 1:
(2744) * (8.621 x 10^(-8)) / (81)^0
And since any non-zero number raised to the power of 0 is equal to 1, our expression becomes:
(2744) * (8.621 x 10^(-8)) / 1
Simplifying further:
(2744) * (8.621 x 10^(-8))
Now, multiplying these numbers:
= 23634.824 x 10^(-8)
= 2.363 x 10^(-3)
Thus, the simplified fraction form of the expression (14^3 * 27^(-7))^(0/3^4) with no remaining exponents is 2.363/1, which can further be simplified as 2363/1000 (by multiplying numerator and denominator by 1000).
So, the final answer is 2363/1000.
Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅27^−7)^0/3^4 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
9 answers
thats wrong
My apologies for the error. Let's start again and apply the properties of integer exponents correctly.
We start with the expression
(14^3 * 27^(-7))^(0/3^4).
First, let's simplify the exponents inside the parentheses:
14^3 = 14 * 14 * 14 = 2744,
27^(-7) = 1 / 27^7.
Now, our expression becomes:
(2744 * (1 / 27^7))^(0/3^4).
Next, we simplify the exponent outside the parentheses:
0/3^4 = 0.
Now our expression becomes:
(2744 * (1 / 27^7))^0.
Any expression raised to the power of 0 is equal to 1, so our expression simplifies to:
1.
Therefore, the equivalent expression is 1.
In fraction form, this is 1/1, which simplifies to 1.
We start with the expression
(14^3 * 27^(-7))^(0/3^4).
First, let's simplify the exponents inside the parentheses:
14^3 = 14 * 14 * 14 = 2744,
27^(-7) = 1 / 27^7.
Now, our expression becomes:
(2744 * (1 / 27^7))^(0/3^4).
Next, we simplify the exponent outside the parentheses:
0/3^4 = 0.
Now our expression becomes:
(2744 * (1 / 27^7))^0.
Any expression raised to the power of 0 is equal to 1, so our expression simplifies to:
1.
Therefore, the equivalent expression is 1.
In fraction form, this is 1/1, which simplifies to 1.
still wrong
Apologies once again for the mistake. Let's analyze the expression again and apply the properties of integer exponents correctly.
We have the expression:
(14^3 * 27^(-7))^(0/3^4).
First, let's simplify the exponents inside the parentheses:
14^3 = 14 * 14 * 14 = 2744,
27^(-7) = 1/27^7,
so the expression becomes:
(2744 * (1/27^7))^(0/3^4).
Next, let's simplify the exponent outside the parentheses:
0/3^4 = 0.
Now the expression becomes:
(2744 * (1/27^7))^0.
According to the property (a * b)^c = a^c * b^c, we can rewrite the expression as:
(2744^0) * ((1/27^7)^0).
Any non-zero number raised to the power of 0 is equal to 1, so we have:
1 * (1/27^7)^0.
And any non-zero number (in this case, 1/27^7) raised to the power of 0 is also equal to 1, so we have:
1 * 1.
Therefore, the equivalent expression is 1.
In fraction form, this is 1/1, which simplifies to 1.
So, the correct answer is 1.
We have the expression:
(14^3 * 27^(-7))^(0/3^4).
First, let's simplify the exponents inside the parentheses:
14^3 = 14 * 14 * 14 = 2744,
27^(-7) = 1/27^7,
so the expression becomes:
(2744 * (1/27^7))^(0/3^4).
Next, let's simplify the exponent outside the parentheses:
0/3^4 = 0.
Now the expression becomes:
(2744 * (1/27^7))^0.
According to the property (a * b)^c = a^c * b^c, we can rewrite the expression as:
(2744^0) * ((1/27^7)^0).
Any non-zero number raised to the power of 0 is equal to 1, so we have:
1 * (1/27^7)^0.
And any non-zero number (in this case, 1/27^7) raised to the power of 0 is also equal to 1, so we have:
1 * 1.
Therefore, the equivalent expression is 1.
In fraction form, this is 1/1, which simplifies to 1.
So, the correct answer is 1.
try again
Apologies for the confusion. Let's reanalyze the expression and apply the properties of integer exponents correctly.
We have the expression:
(14^3 * 27^(-7))^(0/3^4).
First, let's simplify the exponents inside the parentheses:
14^3 = 14 * 14 * 14 = 2744,
27^(-7) = 1 / 27^7.
The expression now becomes:
(2744 * (1 / 27^7))^(0/3^4).
Next, let's simplify the exponent outside the parentheses:
0/3^4 = 0/81 = 0.
Now the expression becomes:
(2744 * (1 / 27^7))^0.
According to the property (a^m)^n = a^(m * n), we can rewrite the expression as:
2744^0 * (1 / 27^7)^0.
Any non-zero number raised to the power of 0 is equal to 1, so we have:
1 * 1.
Therefore, the equivalent expression is 1.
In fraction form, this is 1/1, which simplifies to 1.
Therefore, the simplified fraction form of the expression (14^3 * 27^(-7))^0/(3^4) with no remaining exponents is 1.
We have the expression:
(14^3 * 27^(-7))^(0/3^4).
First, let's simplify the exponents inside the parentheses:
14^3 = 14 * 14 * 14 = 2744,
27^(-7) = 1 / 27^7.
The expression now becomes:
(2744 * (1 / 27^7))^(0/3^4).
Next, let's simplify the exponent outside the parentheses:
0/3^4 = 0/81 = 0.
Now the expression becomes:
(2744 * (1 / 27^7))^0.
According to the property (a^m)^n = a^(m * n), we can rewrite the expression as:
2744^0 * (1 / 27^7)^0.
Any non-zero number raised to the power of 0 is equal to 1, so we have:
1 * 1.
Therefore, the equivalent expression is 1.
In fraction form, this is 1/1, which simplifies to 1.
Therefore, the simplified fraction form of the expression (14^3 * 27^(-7))^0/(3^4) with no remaining exponents is 1.
it isnt 1
I apologize for the error. Let's reanalyze the expression again and apply the properties of integer exponents correctly.
We have the expression:
(14^3 * 27^(-7))^0 / 3^4
First, let's simplify the exponents inside the parentheses:
14^3 = 14 * 14 * 14 = 2744
27^(-7) = 1 / 27^7
Now, the expression becomes:
(2744 * (1 / 27^7))^0 / 3^4
Next, let's simplify the numerator:
(2744 * (1 / 27^7))^0 = 1^0 = 1
Now, the expression becomes:
1 / 3^4
Next, let's simplify the denominator:
3^4 = 3 * 3 * 3 * 3 = 81
Now, the expression becomes:
1 / 81
Therefore, the equivalent expression is 1 / 81.
In fraction form, this remains as 1 / 81.
We have the expression:
(14^3 * 27^(-7))^0 / 3^4
First, let's simplify the exponents inside the parentheses:
14^3 = 14 * 14 * 14 = 2744
27^(-7) = 1 / 27^7
Now, the expression becomes:
(2744 * (1 / 27^7))^0 / 3^4
Next, let's simplify the numerator:
(2744 * (1 / 27^7))^0 = 1^0 = 1
Now, the expression becomes:
1 / 3^4
Next, let's simplify the denominator:
3^4 = 3 * 3 * 3 * 3 = 81
Now, the expression becomes:
1 / 81
Therefore, the equivalent expression is 1 / 81.
In fraction form, this remains as 1 / 81.