4^0 x 5^-2 devided by (2)^-3
To solve this expression, we need to follow the order of operations which states that we should perform any calculations inside parentheses first, then exponents, then multiplication/division from left to right, and finally addition/subtraction from left to right.
The expression is:
4^0 x 5^-2 / (2)^-3
First, we simplify the exponents:
4^0 = 1 because any number raised to the power of 0 is equal to 1.
5^-2 = 1 / 5^2 = 1 / 25 = 0.04
(2)^-3 = 1 / 2^3 = 1 / 8 = 0.125
Now, plug in the simplified values:
1 x 0.04 / 0.125
Next, perform the division:
0.04 / 0.125 = 0.32
Therefore, 4^0 x 5^-2 / (2)^-3 = 0.32.
could you convert that into a simple fraction
Certainly! To convert the decimal 0.32 into a simple fraction, we can write it as 32/100 and then simplify it.
Since both 32 and 100 are divisible by 4, we can divide both numerator and denominator by 4:
32/4 = 8
100/4 = 25
Therefore, the simple fraction equivalent of 0.32 is 8/25.
0.32 is incorrect
Apologies for the mistake. Let's convert 0.32 into a simple fraction correctly.
To convert a decimal to a fraction, we can use the place value of the decimal. In this case, the decimal goes up to two decimal places, so we can write it as:
0.32 = 32/100
The fraction 32/100 is not yet in simplest form. We can simplify it by dividing both the numerator and denominator by their greatest common divisor, which is 4:
32 ÷ 4 = 8
100 ÷ 4 = 25
Therefore, the simplified fraction equivalent of 0.32 is 8/25.
Apply the Properties of Integer Exponents to generate equivalent expressions to 4^0 x 5^−2/(−2)^−3 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 convert the expression 4^0 x 5^−2/(−2)^−3 into an equivalent expression with only positive exponents, we can use the following rules:
1. Any number raised to the power of 0 is equal to 1.
2. A negative exponent can be rewritten as the reciprocal of the positive exponent.
Let's break down the expression step by step:
1. 4^0 = 1 since any number raised to the power of 0 is equal to 1.
2. 5^−2 can be rewritten as 1/5^2 since a negative exponent becomes the reciprocal of the positive exponent.
Therefore, 5^−2 = 1/5^2 = 1/25.
3. (−2)^−3 can be rewritten as 1/(−2)^3 since a negative exponent becomes the reciprocal of the positive exponent.
Therefore, (−2)^−3 = 1/(−2)^3 = 1/(-2)^3 = 1/(-8) = -1/8.
Now, we substitute the simplified expressions back into the original expression:
1 x 1/25 / (-1/8) = 1/25 x (-8/-1) = 1/25 x 8 = 8/25.
Therefore, the simplified fraction equivalent of 4^0 x 5^−2/(−2)^−3 with only positive exponents is 8/25.
8/25 is incorrect
I apologize for the mistake. Let's correct the solution.
To simplify the expression 4^0 x 5^(-2) / (-2)^(-3) using the properties of integer exponents, we can rewrite the negative exponents as the reciprocals with positive exponents:
4^0 x 5^(-2) / (-2)^(-3) = 1 x (1/5^2) / (1/(-2)^3)
Since any number raised to the power of 0 is equal to 1:
= 1 x 1/5^2 / (1/(-2)^3)
Simplifying the exponents:
= 1 x 1/25 / (1/(-8))
Now, we can divide by a fraction by multiplying by its reciprocal:
= 1 x 1/25 x (-8/1)
Multiplying the numerators and denominators:
= (-8/25)
Therefore, the simplified fraction equivalent of 4^0 x 5^(-2) / (-2)^(-3) is -8/25.
that is correct!
I'm glad the solution is correct! If you have any more questions or need further assistance, feel free to ask.
Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅27^−7)^0/3^4 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 to the expression (14^3⋅27^−7)^0/3^4 with only positive exponents, we can use the following rules:
1. Any number raised to the power of 0 is equal to 1.
2. A negative exponent can be rewritten as the reciprocal of the positive exponent.
Let's break down the expression step by step:
1. (14^3⋅27^−7)^0/3^4
2. Since any number raised to the power of 0 is equal to 1, we can simplify to: 1/3^4
3. We can rewrite the negative exponent as the reciprocal of the positive exponent: 1/3^4 = 1/81
Therefore, the simplified fraction equivalent of (14^3⋅27^−7)^0/3^4 with only positive exponents is 1/81.