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)
(143⋅27−7)034=
To generate equivalent expressions with only positive exponents, we can make use of the properties of integer exponents.
First, we can rewrite 143⋅27 as (11⋅13)⋅(3^3).
Next, we can rewrite (3^3)^(-7) as 3^(3*(-7)).
Applying the properties of exponents, we have:
(143⋅27^(-7))^034 = ((11⋅13)⋅(3^3))^034
= (11^034)⋅(13^034)⋅(3^(3*34))
= 11^(0)⋅13^(0)⋅(3^(102))
Any number raised to the power of 0 is equal to 1, so we have:
= 1⋅1⋅(3^(102))
= 3^(102)
Therefore, the simplified fraction of the expression (143⋅27^(-7))^034 is 3^(102).
are you sure
My apologies for the incorrect response. Let's try again.
To generate equivalent expressions with only positive exponents, we can use the property that (a^m)^n = a^(m*n).
First, let's rewrite 143⋅27 as (11⋅13)⋅(3^3).
So we have ((11⋅13)⋅(3^3))^(-7) * 3^4.
Applying the property, we can simplify the expression:
= (11⋅13)^(-7*(3^3)) * 3^4.
Now, simplifying further:
= (11^(-7*(3^3)) * 13^(-7*(3^3)) * 3^(-7*(3^3))) * 3^4.
Since any number raised to the power of 0 is 1, we can simplify the expression as follows:
= 1 * 1 * 1 * 3^4
= 3^4
= 81.
Therefore, the simplified fraction of the expression (143⋅27^(-7))^034 is 81.
wrong
I apologize for the mistake in my previous response. Let's try again.
To generate equivalent expressions with only positive exponents, we can use the property that (a^m)^n = a^(m*n).
First, let's rewrite 143⋅27 as (11⋅13)⋅(3^3).
So we have ((11⋅13)⋅(3^3))^(-7) * 3^4.
Using the property mentioned earlier, we can simplify the expression:
= (11⋅13)^(-7*3^3) * 3^4.
Now, let's simplify further:
= (11^(-7*3^3) * 13^(-7*3^3)) * 3^(-7*3^3) * 3^4.
Since we have the same base, we can add the exponents when multiplying like bases:
= 11^(-7*27) * 13^(-7*27) * 3^(-7*27) * 3^4.
Simplifying the exponent:
= 11^(-189) * 13^(-189) * 3^(-189) * 3^4.
Now, we can simplify further by combining the like bases:
= (11 * 13 * 3)^(-189) * 3^4.
= (429)^(-189) * 3^4.
To simplify further, we can write 429 as a fraction:
= (429/1)^(-189) * 3^4
= (1/429)^189 * 3^4.
Therefore, the equivalent expression with only positive exponents is (1/429)^189 * 3^4.