Use the commutative and associative properties of real numbers and the properties of exponents to simplify the expression.
33R^2T^7/22RT^4
To simplify the expression 33R^2T^7/22RT^4, we can start by applying the commutative property of multiplication to rearrange the terms:
33R^2T^7/22RT^4 = (33/22)(R^2/R)(T^7/T^4)
Now, we can simplify the exponents using the properties of exponents:
(R^2/R) = R^(2-1) = R^1 = R
(T^7/T^4) = T^(7-4) = T^3
Substituting these simplified terms back into the expression, we have:
(33/22)(R^2/R)(T^7/T^4) = (33/22)(R)(T^3)
Finally, we can apply the associative property of multiplication to group the terms:
(33/22)(R)(T^3) = (33R/22)(T^3)
Therefore, the simplified expression is (33R/22)(T^3).
To simplify the expression 33R^2T^7 / 22RT^4, we can use the properties of exponents and the commutative and associative properties of real numbers.
Step 1: Simplify the coefficients
The coefficient of 33 and 22 have a common factor of 11. Divide both coefficients by 11:
(33R^2T^7) / (22RT^4) = (3R^2T^7) / (2RT^4)
Step 2: Simplify the variables
Since we have R^2 in the numerator and RT in the denominator, we can cancel one R from each:
(3R^2T^7) / (2RT^4) = (3R^(2-1)T^7) / (2T^4)
Simplifying this further, we get:
(3RT^7) / (2T^4)
Step 3: Simplify the exponents
Since we are dividing T^7 by T^4, we subtract the exponents:
(3RT^7) / (2T^4) = (3R) / (2T^(7-4))
Simplifying further, we get:
(3R) / (2T^3)
Therefore, the simplified form of the expression 33R^2T^7 / 22RT^4 is (3R) / (2T^3).
To simplify the given expression, let's use the commutative property of real numbers to rearrange the terms:
33R^2T^7 / 22RT^4
Next, we can use the associative property of real numbers to group the terms in a helpful way:
(33/22) * (R^2 / R) * (T^7 / T^4)
Now, let's simplify each component individually:
(33/22) simplifies to 3/2
(R^2 / R) simplifies to R^(2-1) which is equal to R^1 or just R
(T^7 / T^4) simplifies to T^(7-4) which is equal to T^3
Combining all these simplified components, we get:
(3/2) * R * T^3
This is the simplified expression.
Simplify.
7x^-2
To simplify 7x^-2, we can use the property of negative exponents, which states that x^-n is equal to 1/x^n.
Using this property, we can rewrite the expression as:
7 * 1/x^2
To combine this expression, we can multiply the coefficients:
7/x^2
Therefore, the simplified form of 7x^-2 is 7/x^2.
Simplify.
y^-5
To simplify y^-5, we can use the property of negative exponents, which states that y^-n is equal to 1/y^n.
Using this property, we can rewrite the expression as:
1/y^5
Therefore, the simplified form of y^-5 is 1/y^5.
Simplify the expression.
(2n3m2)3(mn3)2
To simplify the expression (2n^3m^2)^3(mn^3)^2, we can apply the rules of exponentiation and simplify each term separately.
First, let's simplify (2n^3m^2)^3:
(2n^3m^2)^3 = 2^3 * (n^3)^3 * (m^2)^3
= 8 * n^(3*3) * m^(2*3)
= 8n^9m^6
Next, let's simplify (mn^3)^2:
(mn^3)^2 = (m)^2 * (n^3)^2
= m^2 * n^(3*2)
= m^2 * n^6
Now, we can combine the simplified terms:
(2n^3m^2)^3(mn^3)^2 = (8n^9m^6)(m^2n^6)
= 8n^9m^6m^2n^6
= 8n^9n^6m^6m^2
= 8n^(9+6)m^(6+2)
= 8n^15m^8
Therefore, the simplified form of the expression (2n^3m^2)^3(mn^3)^2 is 8n^15m^8.
Simplify the expression. Write the answer in exponent form.
t^5 ∙ t^7
To simplify the expression t^5 ∙ t^7, we can use the property of exponents that states: when multiplying powers with the same base, you add the exponents.
Applying this property to the given expression, we have:
t^5 ∙ t^7 = t^(5+7) = t^12
Therefore, the simplified form of the expression t^5 ∙ t^7 is t^12.
Simplify.
(8/7)^-3
To simplify (8/7)^-3, we can use the property of negative exponents, which states that (a/b)^-n is equal to (b/a)^n.
Applying this property, we can rewrite the expression as:
(7/8)^3
To evaluate this expression, we raise both the numerator, 7, and the denominator, 8, to the power of 3:
(7^3) / (8^3)
Simplifying further, we have:
343 / 512
Therefore, the simplified form of (8/7)^-3 is 343/512.
Use the commutative and associative properties of real numbers and the properties of exponents to simplify the expression.
(-10y^5x^7)(7x^2y^10)
To simplify the expression (-10y^5x^7)(7x^2y^10), we can use the commutative and associative properties of real numbers to rearrange and group the terms:
(-10y^5x^7)(7x^2y^10) = -10 * 7 * (y^5 * y^10) * (x^7 * x^2)
Now, we can simplify the coefficients:
-10 * 7 = -70
Next, we can simplify the variables by adding the exponents for each term:
y^5 * y^10 = y^(5+10) = y^15
x^7 * x^2 = x^(7+2) = x^9
Combining the simplified terms, we have:
-70 * y^15 * x^9
Therefore, the simplified form of the expression (-10y^5x^7)(7x^2y^10) is -70y^15x^9.
Simplify the expression.
(4X^6)^2
To simplify the expression (4x^6)^2, we can apply the power of a power rule, which states that (a^b)^c is equal to a^(b*c).
Applying this rule, we have:
(4x^6)^2 = 4^2 * (x^6)^2
= 16 * x^(6*2)
= 16 * x^12
Therefore, the simplified form of the expression (4x^6)^2 is 16x^12.
Simplify the expression. Write the answer in exponent form.
X^9X^8/X^14
To simplify the expression X^9 * X^8 / X^14, we can use the properties of exponents. When dividing two numbers with the same base, we subtract the exponents.
X^9 * X^8 / X^14 = X^(9 + 8 - 14) = X^3
Therefore, the simplified expression is X^3.
Solve the equation.
9 + 6z = 49 - 2z
To solve the equation 9 + 6z = 49 - 2z, we can start by combining like terms by adding 2z to both sides of the equation.
9 + 6z + 2z = 49 - 2z + 2z
This simplifies to:
9 + 8z = 49
Next, we can isolate the variable by subtracting 9 from both sides of the equation.
9 + 8z - 9 = 49 - 9
This simplifies to:
8z = 40
Finally, we can solve for z by dividing both sides of the equation by 8.
(8z) / 8 = 40 / 8
This simplifies to:
z = 5
Therefore, the solution to the equation 9 + 6z = 49 - 2z is z = 5.
Simplify.
(6z)^-1
To simplify (6z)^-1, we can use the property of negative exponents, which states that (a^b)^-1 is equal to 1/(a^b).
Applying this property, we can rewrite the expression as:
1/(6z)^1
Since any term raised to the power of 1 is equal to itself, we can simplify further:
1/(6z)
Therefore, the simplified form of (6z)^-1 is 1/(6z).
Simplify the expression. Write your answer with positive exponents only.
(4A^5B)^-2/(A^2B^5)^-5
To simplify the expression (4A^5B)^-2 / (A^2B^5)^-5, we can use the property of negative exponents and apply the rule for dividing powers with the same base by subtracting exponents.
First, let's apply the negative exponents property:
(1 / (4A^5B)^2) / (1 / (A^2B^5)^5)
Next, let's raise each expression to the power of -1 to remove the negative exponents:
((4A^5B)^2)^-1 / ((A^2B^5)^5)^-1
Simplifying the exponents:
(4^2A^(5*2)B^(1*2))^-1 / (A^(2*5)B^(5*5))^-1
(16A^10B^2)^-1 / (A^10B^25)^-1
Now, we can switch the numerator and denominator by applying the reciprocal property:
(A^10B^25) / (16A^10B^2)
Next, let's combine like terms:
A^10 / 16A^10 * B^25 / B^2
Simplifying the exponents again:
1 / 16 * A^(10-10) * B^(25-2)
1 / 16 * A^0 * B^23
Any term raised to the power of 0 is equal to 1, so A^0 = 1:
1 / 16 * 1 * B^23
Simplifying further:
B^23 / 16
Therefore, the simplified form of the expression (4A^5B)^-2 / (A^2B^5)^-5 is B^23 / 16
Simplify. Write your answer in exponent form.
(Z^3)^7
To simplify (Z^3)^7, we can apply the property of exponentiation, which states that when a power is raised to another power, we multiply the exponents.
Applying this property, we have:
(Z^3)^7 = Z^(3*7) = Z^21
Therefore, the simplified form of (Z^3)^7 is Z^21.
Evaluate the expression.
-5^2
To evaluate the expression -5^2, we need to follow the order of operations.
According to the order of operations (which states that exponents should be evaluated before multiplication), we first evaluate the exponent, and then apply the negation.
-5^2 = -(5^2)
Next, we evaluate the exponent 5^2:
5^2 = 5 * 5 = 25
Finally, we apply the negation:
-(5^2) = -25
Therefore, the value of the expression -5^2 is -25.
Solve the equation.
5y + 1(y + 3) = 9
To solve the equation 5y + 1(y + 3) = 9, we can begin by simplifying the equation:
5y + 1(y + 3) = 9
Next, distribute the 1 to each term inside the parentheses:
5y + y + 3 = 9
Now, combine like terms:
6y + 3 = 9
To isolate the variable term, subtract 3 from both sides:
6y + 3 - 3 = 9 - 3
This simplifies to:
6y = 6
Finally, divide both sides of the equation by 6 to solve for y:
(6y) / 6 = 6 / 6
The simplified equation is:
y = 1
Thus, the solution to the equation 5y + 1(y + 3) = 9 is y = 1.
simplify
-50y^0
To simplify -50y^0, we need to apply the property of any number raised to the power of 0, which states that any number (except 0) raised to the power of 0 is equal to 1.
Therefore, y^0 is equal to 1.
Simplifying further:
-50y^0 = -50 * 1 = -50
Therefore, the simplified form of -50y^0 is -50.
simplify
(-3y^3)^0
To simplify (-3y^3)^0, we can use the property of any number (except 0) raised to the power of 0, which states that any number (except 0) raised to the power of 0 is equal to 1.
Therefore, (-3y^3)^0 is equal to 1.
Therefore, the simplified form of (-3y^3)^0 is 1.
simplify expression
(2a^6b^7/a^4b^6)^3
To simplify the expression (2a^6b^7 / a^4b^6)^3, we can apply the properties of exponents and division.
First, let's divide the terms inside the parentheses:
(2a^6b^7 / a^4b^6)^3 = (2/a^4) * (a^6 / b^6b^7)
Now, let's simplify each term individually:
2/a^4 = 2a^(-4)
a^6 / b^6b^7 = a^6 / b^(6+7) = a^6 / b^13
Now, let's combine the simplified terms:
(2a^(-4)) * (a^6 / b^13)
Next, let's use the product of powers rule for multiplying terms with the same base:
2a^(-4) * a^6 = 2a^(-4+6) = 2a^2
Therefore, the simplified expression is:
2a^2 / b^13
Question 19 options:
A)
2a^6b^3
B)
2a^14bv15
C)
8a^6b^3
D)
8a^2b