To apply the properties of integer exponents, we can start by simplifying the expression inside the parentheses first:
(4^0 ⋅ 5^(-2))^(-5/(-2)^(-3)).
Since any number raised to the power of 0 is equal to 1, we have:
(1 ⋅ 5^(-2))^(-5/(-2)^(-3)).
Next, we simplify the negative exponent by taking the reciprocal of the base and changing the sign of the exponent:
(1 ⋅ 1/(5^2))^(-5/(-2)^(-3)).
Simplifying further:
(1 ⋅ 1/25)^(-5/(-2)^(-3)).
Next, we simplify the expression inside the exponent:
1/25^(-5/(-2)^(-3)).
Now, let's apply the property of negative exponents by taking the reciprocal of the base and changing the sign of the exponent:
(25)^(5/(-2)^(-3)).
Next, we simplify the exponent:
(25)^(5/((-1)^(-3))).
Since -1 raised to any odd power is equal to -1, we have:
(25)^(5/(-1)).
Simplifying further:
(25)^(-5).
Finally, we apply the property of negative exponents:
1/(25^5).
Therefore, the equivalent expression with only positive exponents is 1/(25^5), and this is also the simplified fraction form of the expression.
Apply the Properties of Integer Exponents to generate equivalent expressions to (4^0 ⋅
5^−2)^−5/(-2)^-3
with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
9 answers
wrong
Apologies for the mistake. Let's correct the solution.
To apply the properties of integer exponents, we start by simplifying the expression inside the parentheses first:
(4^0 ⋅ 5^(-2))^(-5/(-2)^(-3)).
Since any number raised to the power of 0 is equal to 1, we have:
(1 ⋅ 5^(-2))^(-5/(-2)^(-3)).
Next, we simplify the negative exponent by taking the reciprocal of the base and changing the sign of the exponent:
(1 ⋅ 1/(5^2))^(-5/(-2)^(-3)).
Simplifying further:
(1 ⋅ 1/25)^(-5/(-2)^(-3)).
Next, we simplify the expression inside the exponent:
1/25^(-5/(-2)^(-3)).
Now, let's simplify the exponent:
1/(25^(-5) ⋅ (-2)^3).
To apply the property of negative exponents, we can move the bases with negative exponents to the denominator and change the signs of the exponents:
1/((1/(25^5)) ⋅ (1/(-2)^3)).
Simplifying further:
1/((1/(25^5)) ⋅ (1/(-8))).
We can multiply the reciprocals together:
1/(1/(25^5) ⋅ (-1/8)).
To divide fractions, we multiply by the reciprocal of the denominator:
(1 ⋅ 8)/(1 ⋅ 25^5).
Simplifying further:
8/25^5.
Therefore, the equivalent expression with only positive exponents is 8/25^5, and this is the simplified fraction form of the expression.
To apply the properties of integer exponents, we start by simplifying the expression inside the parentheses first:
(4^0 ⋅ 5^(-2))^(-5/(-2)^(-3)).
Since any number raised to the power of 0 is equal to 1, we have:
(1 ⋅ 5^(-2))^(-5/(-2)^(-3)).
Next, we simplify the negative exponent by taking the reciprocal of the base and changing the sign of the exponent:
(1 ⋅ 1/(5^2))^(-5/(-2)^(-3)).
Simplifying further:
(1 ⋅ 1/25)^(-5/(-2)^(-3)).
Next, we simplify the expression inside the exponent:
1/25^(-5/(-2)^(-3)).
Now, let's simplify the exponent:
1/(25^(-5) ⋅ (-2)^3).
To apply the property of negative exponents, we can move the bases with negative exponents to the denominator and change the signs of the exponents:
1/((1/(25^5)) ⋅ (1/(-2)^3)).
Simplifying further:
1/((1/(25^5)) ⋅ (1/(-8))).
We can multiply the reciprocals together:
1/(1/(25^5) ⋅ (-1/8)).
To divide fractions, we multiply by the reciprocal of the denominator:
(1 ⋅ 8)/(1 ⋅ 25^5).
Simplifying further:
8/25^5.
Therefore, the equivalent expression with only positive exponents is 8/25^5, and this is the simplified fraction form of the expression.
still wrong remove all exponents
Apologies for the confusion. Let's remove all exponents to simplify the expression.
Starting with the original expression:
(4^0 ⋅ 5^(-2))^(-5/(-2)^(-3))
We know that any number raised to 0 is equal to 1, so we have:
(1 ⋅ 1/(5^2))^(-5/(-2)^(-3))
Simplifying further, we have:
(1 ⋅ 1/25)^(-5/((-1)^(-3)))
Since the reciprocal of 25 is 1/25, we can rewrite the expression as:
(1/25)^(-5/((-1)^(-3)))
Next, let's simplify the negative exponents:
(1/25)^(-5/1)
We know that any number raised to 1 is equal to the number itself, so:
1/(1/25)^5
Now, let's remove the parentheses by taking the reciprocal of 1/25 and raising it to the power of 5:
1/(1^5/25^5)
Since any number raised to the power of 1 is equal to the number itself, we have:
1/(1/25^5)
Again, let's simplify the reciprocal:
25^5/1
Finally, our simplified expression is:
25^5
Therefore, the equivalent expression with only positive exponents is 25^5, which is equal to 3,906,250.
Starting with the original expression:
(4^0 ⋅ 5^(-2))^(-5/(-2)^(-3))
We know that any number raised to 0 is equal to 1, so we have:
(1 ⋅ 1/(5^2))^(-5/(-2)^(-3))
Simplifying further, we have:
(1 ⋅ 1/25)^(-5/((-1)^(-3)))
Since the reciprocal of 25 is 1/25, we can rewrite the expression as:
(1/25)^(-5/((-1)^(-3)))
Next, let's simplify the negative exponents:
(1/25)^(-5/1)
We know that any number raised to 1 is equal to the number itself, so:
1/(1/25)^5
Now, let's remove the parentheses by taking the reciprocal of 1/25 and raising it to the power of 5:
1/(1^5/25^5)
Since any number raised to the power of 1 is equal to the number itself, we have:
1/(1/25^5)
Again, let's simplify the reciprocal:
25^5/1
Finally, our simplified expression is:
25^5
Therefore, the equivalent expression with only positive exponents is 25^5, which is equal to 3,906,250.
why is it not a fraction
Apologies for the oversight. Let's correct the solution.
Starting with the original expression:
(4^0 ⋅ 5^(-2))^(-5/(-2)^(-3))
We know that any number raised to 0 is equal to 1, so we have:
(1 ⋅ 1/(5^2))^(-5/(-2)^(-3))
Simplifying further, we have:
(1 ⋅ 1/25)^(-5/((-1)^(-3)))
Since the reciprocal of 25 is 1/25, we can rewrite the expression as:
(1/25)^(-5/((-1)^(-3)))
Next, let's simplify the negative exponents:
(1/25)^(-5/(1))
We know that any number raised to 1 is equal to the number itself, so:
(1/25)^(-5)
To remove the negative exponent, we can take the reciprocal:
25^(5)
Therefore, the equivalent expression with only positive exponents is 25^5.
The final answer is 25^5, which is equal to 9,765,625.
Starting with the original expression:
(4^0 ⋅ 5^(-2))^(-5/(-2)^(-3))
We know that any number raised to 0 is equal to 1, so we have:
(1 ⋅ 1/(5^2))^(-5/(-2)^(-3))
Simplifying further, we have:
(1 ⋅ 1/25)^(-5/((-1)^(-3)))
Since the reciprocal of 25 is 1/25, we can rewrite the expression as:
(1/25)^(-5/((-1)^(-3)))
Next, let's simplify the negative exponents:
(1/25)^(-5/(1))
We know that any number raised to 1 is equal to the number itself, so:
(1/25)^(-5)
To remove the negative exponent, we can take the reciprocal:
25^(5)
Therefore, the equivalent expression with only positive exponents is 25^5.
The final answer is 25^5, which is equal to 9,765,625.
your answer must be a fraction
Apologies for the confusion. Let's correct the solution.
Starting with the original expression:
(4^0 ⋅ 5^(-2))^(-5/(-2)^(-3))
We know that any number raised to 0 is equal to 1, so we have:
(1 ⋅ 1/(5^2))^(-5/(-2)^(-3))
Simplifying further, we have:
(1 ⋅ 1/25)^(-5/((-1)^(-3)))
Since the reciprocal of 25 is 1/25, we can rewrite the expression as:
(1/25)^(-5/((-1)^(-3)))
Next, let's simplify the negative exponents:
(1/25)^(-5/(1))
We know that any number raised to 1 is equal to the number itself, so:
(1/25)^(-5)
To remove the negative exponent, we can take the reciprocal:
25^(5)
Therefore, the equivalent expression with only positive exponents is 25^5.
Now, to express this as a simplified fraction with no remaining exponents, we can write it as:
1 / 25^(-5).
To simplify this, we can bring 25^(-5) to the numerator by changing the sign of the exponent:
1 / (1 / 25^5).
To divide by a fraction, we can multiply by its reciprocal:
1 * 25^5 / 1.
Simplifying further, we get:
25^5.
Therefore, the equivalent expression as a simplified fraction with no remaining exponents is 25^5.
Starting with the original expression:
(4^0 ⋅ 5^(-2))^(-5/(-2)^(-3))
We know that any number raised to 0 is equal to 1, so we have:
(1 ⋅ 1/(5^2))^(-5/(-2)^(-3))
Simplifying further, we have:
(1 ⋅ 1/25)^(-5/((-1)^(-3)))
Since the reciprocal of 25 is 1/25, we can rewrite the expression as:
(1/25)^(-5/((-1)^(-3)))
Next, let's simplify the negative exponents:
(1/25)^(-5/(1))
We know that any number raised to 1 is equal to the number itself, so:
(1/25)^(-5)
To remove the negative exponent, we can take the reciprocal:
25^(5)
Therefore, the equivalent expression with only positive exponents is 25^5.
Now, to express this as a simplified fraction with no remaining exponents, we can write it as:
1 / 25^(-5).
To simplify this, we can bring 25^(-5) to the numerator by changing the sign of the exponent:
1 / (1 / 25^5).
To divide by a fraction, we can multiply by its reciprocal:
1 * 25^5 / 1.
Simplifying further, we get:
25^5.
Therefore, the equivalent expression as a simplified fraction with no remaining exponents is 25^5.