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