9⋅(−33)^0+3/2(8−27^0)
To solve the expression, we need to follow the order of operations.
First, we have to evaluate any exponents. Any number raised to the power of 0 is equal to 1. So, (-33)^0 equals 1.
Let's substitute that value back into the expression:
9 * 1 + 3/2 * (8 - 1)
Next, we can simplify within the parentheses:
9 + 3/2 * (7)
Now, we simplify the multiplication:
9 + 21/2
We need to have a common denominator to add the fractions:
9 + (21/2) * (2/2) = 9 + 42/2
Now, we can add the fractions:
9 + 42/2 = 9 + 21 = 30
So, 9⋅(−33)^0+3/2(8−27^0) simplifies to 30.
9⋅(−33)^0+3/2(8−27^0) = ? ⋅ ? +32( – )
To simplify the given expression, let's first evaluate the exponents.
(-33)^0 is equal to 1, and 27^0 is also equal to 1.
Substituting those values back into the expression, we have:
9 * 1 + 3/2 * (8 - 1) = 9 + 3/2 * 7
Next, let's simplify the multiplication within the parentheses:
9 + 3/2 * 7 = 9 + (3/2) * 7
Multiplying 3/2 by 7, we get:
9 + (3/2) * 7 = 9 + (21/2)
Now, let's bring both fractions to a common denominator by multiplying the first fraction by 2/2:
9 + (21/2) * (2/2) = 9 + (42/2)
Adding the fractions together:
9 + (42/2) = 9 + 21
Finally:
9 + 21 = 30
So, the simplified expression is 30.
Apply the Properties of Integer Exponents to generate equivalent expressions to (7^−3)^7 ⋅ 7^20/6^−2 with only positive exponents, then solve the expression. Provide the answer as an improper fraction.(1 point)
(7^−3)^7 ⋅ 7^20/6^−2=
To apply the properties of integer exponents and simplify the expression, we can first evaluate the exponent inside the parentheses, then simplify the remaining expression using the properties of exponents.
(7^(-3))^7 is equal to (1/7^3)^7
Using the property (a^m)^n = a^(m*n), we can simplify further:
(1/7^3)^7 = 1/(7^3 * 7^3 * 7^3 * 7^3 * 7^3 * 7^3 * 7^3)
Now, let's simplify the expression 7^20/6^(-2):
Using the property a^(-m) = 1/(a^m), we can rewrite the expression as:
7^20/(1/6^2)
To simplify 1/6^2, we can use the property 1/a^m = a^(-m):
1/6^2 = 6^(-2)
Now, we have:
(1/(7^3)^7) * 7^20/6^(-2) = (1/(7^3 * 7^3 * 7^3 * 7^3 * 7^3 * 7^3 * 7^3)) * 7^20 * 6^(-2)
Using the property (a/b) * c = a * c / b, we can rewrite the expression as:
(7^20 * 6^(-2))/(7^3 * 7^3 * 7^3 * 7^3 * 7^3 * 7^3 * 7^3)
Using the property a^m * a^n = a^(m+n):
(7^(20+3*(-2)))/(7^(3+3+3+3+3+3+3))
Simplifying the exponents:
(7^14)/(7^21)
Using the property a^m / a^n = a^(m-n):
7^(14-21) = 7^(-7) = 1/(7^7)
So, the expression (7^(-3))^7 ⋅ 7^20/6^(-2) is equivalent to 1/(7^7) or 1/823543 in the form of an improper fraction.
To solve the expression 9⋅(−33)^0 + 3/2(8−27^0) step-by-step, let's break it down:
Step 1: Start with exponentiation
(-33)^0 equals 1, as any number (except zero) raised to the power of 0 is equal to 1.
So, the expression becomes: 9⋅1 + 3/2(8−1)
Step 2: Simplify the multiplication
9⋅1 equals 9.
Now the expression is: 9 + 3/2(8−1)
Step 3: Simplify the subtraction inside the parentheses
8−1 equals 7.
The expression becomes: 9 + 3/2(7)
Step 4: Simplify the multiplication
3/2 times 7 is equal to 21/2 or 10.5.
Now the expression is: 9 + 10.5
Step 5: Perform the addition
9 + 10.5 equals 19.5.
Therefore, the final result is 19.5.
To simplify the expression 9⋅(−33)^0+3/2(8−27^0), we need to follow the order of operations (PEMDAS), which stands for Parentheses, Exponents, Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right).
Let's break it down step by step:
Step 1: Evaluate any exponents.
In this expression, we have (-33)^0 and 27^0. Any number raised to the power of zero is equal to 1. So, we have:
9⋅1 + 3/2(8 - 1)
Step 2: Simplify the multiplication and division.
In this expression, we have 9⋅1, which is simply equal to 9. Additionally, we have 3/2(8 - 1), which we can simplify as follows:
3/2(8 - 1) = 3/2 * 7 = 21/2
Now, our expression becomes:
9 + 21/2
Step 3: Combine the sum.
To add 9 and 21/2, we need a common denominator. The denominator in 21/2 is 2, so we can rewrite 9 as 9/1 to have a common denominator of 2:
9/1 + 21/2
To add the fractions, we need a common denominator of 2. Let's convert the first fraction:
9/1 * 2/2 = 18/2
Now our expression becomes:
18/2 + 21/2
Step 4: Add the fractions.
Since the two fractions have the same denominator, we can simply add the numerators and keep the denominator:
(18 + 21)/2 = 39/2
Therefore, the simplified expression is 39/2.