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.