Which value is equivalent to 7 multiplied by 5 multiplied by 2 whole over 7 multiplied by 3, the whole raised to the power of 2 multiplied by 5 to the power of 0 over 2 to the power of negative 3, whole to the power of 3 multiplied by 2 to the power of negative 9? (1 point)
10 over 9
20 over 3
100 over 9
700 over 3
The value equivalent to the given expression is 100 over 9.
To simplify the expression, let's break it down step-by-step:
Step 1: Simplify the numerator.
7 multiplied by 5 multiplied by 2 equals 70.
Step 2: Simplify the denominator.
7 multiplied by 3 equals 21.
Step 3: Simplify the whole fraction.
70/21 can be simplified further by dividing both the numerator and denominator by their greatest common divisor, which is 7.
Dividing 70 by 7 equals 10, and dividing 21 by 7 equals 3.
So, 70/21 simplifies to 10/3.
Step 4: Simplify the exponent expressions.
5 to the power of 0 equals 1.
2 to the power of -3 equals 1/2^3, which simplifies to 1/8.
Step 5: Simplify the exponent expression further.
To simplify 3 multiplied by 2 to the power of -9, we have to find the value of 2^-9 first.
2^-9 can be written as 1/2^9, which simplifies to 1/512.
Now, multiplying 3 by 1/512 gives us 3/512.
Step 6: Apply the exponent to the fraction obtained in Step 4.
(1/8)^3 equals (1^3)/(8^3), which simplifies to 1/512.
Step 7: Multiply the numerator and denominator.
Multiplying the numerator and denominator gives us:
(10/3) * (1/512) = 10/1536.
Therefore, the value equivalent to the given expression is 10/1536.
To solve this problem, let's break it down step by step:
Step 1: Simplify the expression within the parentheses.
Within the parentheses, we have 7 multiplied by 5 multiplied by 2, whole over 7 multiplied by 3.
Simplifying this, we get (7 x 5 x 2) / (7 x 3).
Step 2: Simplify the numerator and denominator separately.
In the numerator, we have 7 x 5 x 2 which equals 70.
In the denominator, we have 7 x 3 which equals 21.
Step 3: Rewrite the expression without the parentheses.
We now have 70 / 21.
Step 4: Simplify the division.
To simplify 70 divided by 21, we divide the numerator by the denominator.
70 divided by 21 equals 10 / 3.
Step 5: Simplify any exponents.
The remaining expression involves exponents:
(10 / 3) raised to the power of (2 x 5^0 / 2^-3) to the power of (3 x 2^-9).
To simplify this, we first need to evaluate the exponent within the parentheses: 2 x 5^0 / 2^-3.
Step 6: Compute the exponent within the parentheses.
First, evaluate 5^0, which is equal to 1.
Then, evaluate 2^-3, which is equal to 1 / (2^3) = 1 / 8.
Finally, compute 2 x 1 / (1 / 8) = 2 x 8 = 16.
Step 7: Simplify the remaining exponent.
Now we have (10 / 3)^16 to the power of (3 x 2^-9).
To simplify further, we evaluate 2^-9.
This is equal to 1 / (2^9) = 1 / 512.
Step 8: Compute the final exponent.
Now we have (10 / 3)^16 to the power of (3 x 1 / 512).
Simplify the exponent by multiplying: 3 x 1 / 512 = 3 / 512.
Step 9: Apply the final exponent to the base.
Evaluate (10 / 3)^16^(3 / 512) using a calculator or by using the property (a^b)^c = a^(b*c).
This gives us the final value.
After completing all the steps, the equivalent value is approximately 100 / 9.
Therefore, the correct answer is 100 over 9.