Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅27^−7)^0/34 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
To apply the Properties of Integer Exponents and generate equivalent expressions with only positive exponents, we can use the following rules:
1) When we raise a power to a power, we multiply the exponents. In this case, we have (14^3 * 27^-7) raised to the power of 0, so we can multiply the exponents by 0:
(14^3 * 27^-7)^0 = 14^(3*0) * 27^(-7*0) = 14^0 * 27^0
2) Any number (except 0) raised to the power of 0 is equal to 1. Therefore, 14^0 = 1 and 27^0 = 1:
14^0 * 27^0 = 1 * 1 = 1
So the expression (14^3 * 27^-7)^0 simplifies to 1.
Therefore, the answer to the expression is 1, which is a simplified fraction with no remaining exponents.
that is incorrect
Apologies for the mistake.
Let's apply the properties of integer exponents correctly:
First, let's simplify the expression inside the parentheses:
14^3 * 27^-7
To simplify this expression, we can use the fact that a negative exponent can be rewritten as the reciprocal of the positive exponent:
27^-7 = 1/27^7
Now, let's substitute this back into the original expression:
(14^3 * (1/27^7))^0
Next, we can simplify the expression with positive exponents:
14^3 = 2744
1/27^7 = 1/823543
Substituting these values back into our expression:
(2744 * (1/823543))^0
Now, any non-zero number raised to the power of 0 is equal to 1:
(2744 * (1/823543))^0 = 1
Therefore, the simplified expression is equal to 1.
the answer is not 1
Apologies for the confusion. Let's try again.
We have the expression (14^3 * 27^(-7))^0/34.
To simplify this expression, we can start by applying the property of exponentiation which states that (a^m)^n = a^(m*n). In this case, we have:
(14^3 * 27^(-7))^0 = 14^(3*0) * 27^((-7)*0).
By simplifying the exponents, we get:
14^0 * 27^0.
Next, we know that any number (except 0) raised to the power of 0 is equal to 1:
14^0 * 27^0 = 1 * 1 = 1.
Finally, we need to divide this result by 34:
1/34.
Thus, the simplified fraction with no remaining exponents is 1/34.