To apply the properties of integer exponents, we can use the following rules:
1. Any number raised to the power of 0 is always 1: a^0 = 1, where a is any real number.
2. A negative exponent can be converted to a positive exponent by taking the reciprocal of the base: a^(-n) = 1/a^n, where a is any nonzero real number and n is a positive integer.
Using these rules, we can rewrite the given expression:
4⁰ • 5^-²/(-2)^-³
= 1 • (1/5²)/(1/(-2)³) (Using rule 1 and rule 2)
= 1 • (1/25)/(1/(-8))
= 1 • (-8/25) (Simplifying the fractions)
Therefore, the equivalent expression in positive exponents is 1 • (-8/25) = -8/25.
Apply the properties of integer exponents to generate equivalent expressions to 4⁰ • 5^-²/(-2)^-³ with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
4⁰ • 5^-²/(-2)^-³ =
3 answers
Wrong
I apologize for the mistake. Let's try again:
To apply the properties of integer exponents and generate equivalent expressions with only positive exponents, we can use the following rules:
1. Any number raised to the power of 0 is always 1: a^0 = 1, where a is any nonzero real number.
2. A negative exponent can be converted to a positive exponent by taking the reciprocal of the base: a^(-n) = 1/a^n, where a is any nonzero real number and n is a positive integer.
3. When multiplying two numbers with the same base raised to different exponents, we can add the exponents: a^n * a^m = a^(n+m), where a is any nonzero real number and n, m are integers.
Let's apply these rules to the given expression:
4^0 • 5^(-2) / (-2)^(-3)
Using rule 1, we know that 4^0 is equal to 1:
1 • 5^(-2) / (-2)^(-3)
Now, let's apply rule 2 and convert the negative exponents to positive exponents:
1 • 1/5^2 / 1/(-2)^3
Simplifying the denominator, we have:
1 • 1/5^2 / 1/(-8)
Calculating the values of the exponent:
1 • 1/25 / 1/(-8)
Using rule 3, we know that dividing by a fraction is the same as multiplying by its reciprocal. So we can rewrite the expression as:
1 • 1/25 * (-8/1)
Simplifying the fractions:
1/25 * (-8)
Multiplying the numerator:
-8/25
Therefore, the equivalent expression with only positive exponents is -8/25.
To apply the properties of integer exponents and generate equivalent expressions with only positive exponents, we can use the following rules:
1. Any number raised to the power of 0 is always 1: a^0 = 1, where a is any nonzero real number.
2. A negative exponent can be converted to a positive exponent by taking the reciprocal of the base: a^(-n) = 1/a^n, where a is any nonzero real number and n is a positive integer.
3. When multiplying two numbers with the same base raised to different exponents, we can add the exponents: a^n * a^m = a^(n+m), where a is any nonzero real number and n, m are integers.
Let's apply these rules to the given expression:
4^0 • 5^(-2) / (-2)^(-3)
Using rule 1, we know that 4^0 is equal to 1:
1 • 5^(-2) / (-2)^(-3)
Now, let's apply rule 2 and convert the negative exponents to positive exponents:
1 • 1/5^2 / 1/(-2)^3
Simplifying the denominator, we have:
1 • 1/5^2 / 1/(-8)
Calculating the values of the exponent:
1 • 1/25 / 1/(-8)
Using rule 3, we know that dividing by a fraction is the same as multiplying by its reciprocal. So we can rewrite the expression as:
1 • 1/25 * (-8/1)
Simplifying the fractions:
1/25 * (-8)
Multiplying the numerator:
-8/25
Therefore, the equivalent expression with only positive exponents is -8/25.