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Apply the Properties of Integer Exponents to generate an equivalent expression to 8^0 x 4^3/5^−2 with only positive exponents, then solve the expression. (1 point)
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GPT 3.5
To apply the properties of integer exponents, recall that any non-zero number raised to the power of 0 is equal to 1. Therefore, we can simplify 8^0 to 1.
Next, we can rewrite 4^(3/5)^(-2) using the property of negative exponents, which states that a^(-n) is equal to 1/a^n. Therefore, 4^(3/5)^(-2) can be rewritten as (1/4^(3/5))^2.
So, the equivalent expression is 1 x (1/4^(3/5))^2.
To simplify further, we need to evaluate 1/4^(3/5), which can be rewritten as 4^(-3/5) using the property of negative exponents.
Now, our expression is 1 x (4^(-3/5))^2.
To simplify further, we can multiply the exponents. (-3/5) x 2 = -6/5.
Therefore, the final expression is 1 x 4^(-6/5).
Now, to solve the expression, we can rewrite 4^(-6/5) using the property of negative exponents as 1/4^(6/5).
So, the final expression is 1 x 1/4^(6/5).
To simplify the expression further, we need to evaluate 1/4^(6/5) which can be rewritten as (4^(1/5))^6 using the property of negative exponents.
Now, our expression is 1 x (4^(1/5))^6.
To simplify further, we can multiply the exponents. (1/5) x 6 = 6/5.
Therefore, the final expression is 1 x 4^(6/5).
To solve the expression, we need to evaluate 4^(6/5). We can rewrite 4^(6/5) as (2^2)^(6/5) using the property of exponents.
Now, our expression is 1 x (2^2)^(6/5).
To simplify further, we can multiply the exponents. 2 x (6/ 5) = 12/5.
Therefore, the final expression is 1 x 2^(12/5).
To solve the expression, we need to evaluate 2^(12/5). We can rewrite 2^(12/5) as (2^(1/5))^12 using the property of exponents.
Now, our expression is 1 x (2^(1/5))^12.
To simplify further, we can multiply the exponents. (1/5) x 12 = 12/5.
Therefore, the final expression is 1 x 2^(12/5).
To solve the expression, we need to evaluate 2^(12/5). We can rewrite 2^(12/5) as 2^(2/5 x 6) using the property of exponents.
Now, our expression is 1 x 2^(2/5 x 6).
To simplify further, we can multiply the exponents. (2/5) x 6 = 12/5.
Therefore, the final expression is 1 x 2^(12/5).
So, the equivalent expression to 8^0 x 4^3/5^(-2) with only positive exponents is 2^(12/5).
To solve this expression, we need to evaluate 2^(12/5). This gives us approximately 8.49.
Next, we can rewrite 4^(3/5)^(-2) using the property of negative exponents, which states that a^(-n) is equal to 1/a^n. Therefore, 4^(3/5)^(-2) can be rewritten as (1/4^(3/5))^2.
So, the equivalent expression is 1 x (1/4^(3/5))^2.
To simplify further, we need to evaluate 1/4^(3/5), which can be rewritten as 4^(-3/5) using the property of negative exponents.
Now, our expression is 1 x (4^(-3/5))^2.
To simplify further, we can multiply the exponents. (-3/5) x 2 = -6/5.
Therefore, the final expression is 1 x 4^(-6/5).
Now, to solve the expression, we can rewrite 4^(-6/5) using the property of negative exponents as 1/4^(6/5).
So, the final expression is 1 x 1/4^(6/5).
To simplify the expression further, we need to evaluate 1/4^(6/5) which can be rewritten as (4^(1/5))^6 using the property of negative exponents.
Now, our expression is 1 x (4^(1/5))^6.
To simplify further, we can multiply the exponents. (1/5) x 6 = 6/5.
Therefore, the final expression is 1 x 4^(6/5).
To solve the expression, we need to evaluate 4^(6/5). We can rewrite 4^(6/5) as (2^2)^(6/5) using the property of exponents.
Now, our expression is 1 x (2^2)^(6/5).
To simplify further, we can multiply the exponents. 2 x (6/ 5) = 12/5.
Therefore, the final expression is 1 x 2^(12/5).
To solve the expression, we need to evaluate 2^(12/5). We can rewrite 2^(12/5) as (2^(1/5))^12 using the property of exponents.
Now, our expression is 1 x (2^(1/5))^12.
To simplify further, we can multiply the exponents. (1/5) x 12 = 12/5.
Therefore, the final expression is 1 x 2^(12/5).
To solve the expression, we need to evaluate 2^(12/5). We can rewrite 2^(12/5) as 2^(2/5 x 6) using the property of exponents.
Now, our expression is 1 x 2^(2/5 x 6).
To simplify further, we can multiply the exponents. (2/5) x 6 = 12/5.
Therefore, the final expression is 1 x 2^(12/5).
So, the equivalent expression to 8^0 x 4^3/5^(-2) with only positive exponents is 2^(12/5).
To solve this expression, we need to evaluate 2^(12/5). This gives us approximately 8.49.
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