It's a monomial and we are told to simplify and assume no denominator is equal to zero.
its a -10m-1y0r means -10m to the neg. 1 power and y to the 0 power and r. I don't know how to write the powers. that equation is divided by -14m-7y-3r-4.which means -14m to the -7 power y to the -3 power and r to the-4 power.
What you have described should be written (in the typed format we have to use here) as
-10*m^-1* y^0 *r/[-14*m^-7*y^-3*r^-4]
Any number to the zero power is 1, so you can get rid of the y^0 term in the numnerator.
Exponents in the denominator can be brought to the numerator with a change of sign, and added to whatever exponent is in the numerator attached to the same variable. The -10/-14 can be rewritten as the factor 5/7.
You are then left with
(5/7)m^7*y^3*r^5
To simplify the given expression, let's start by simplifying the powers of each variable.
The given expression is:
(-10m^-1y^0r) / (-14m^-7y^-3r^-4)
To simplify this, we can use the following exponent rules:
1. When dividing two terms with the same base, subtract their exponents.
2. Any non-zero number raised to the power of 0 is equal to 1.
Let's apply these rules step by step:
Step 1: Simplify the variables individually.
a) For "m":
m^-1 divided by m^-7:
According to rule 1, subtract the exponents: (-1) - (-7) = 7 - 1 = 6
So, m^-1 divided by m^-7 is equal to m^6.
b) For "y":
y^0 divided by y^-3:
According to rule 1, subtract the exponents: 0 - (-3) = 0 + 3 = 3
So, y^0 divided by y^-3 is equal to y^3.
c) For "r":
The exponent of r does not change as it is already in the correct form.
Step 2: Combine the simplified variables.
Now, we have:
(-10m^-1y^0r) / (-14m^-7y^-3r^-4)
= (-10 * m^6 * y^3 * r) / (-14 * m^-7 * y^-3 * r^-4)
Step 3: Combine the constants.
(-10 / -14) simplifies to (5 / 7).
Final simplified expression:
(5/7) * (m^6 / m^-7) * (y^3 / y^-3) * r / r^-4
To simplify further, let's use the following rule:
3. When dividing two terms with the same base, subtract their exponents.
Applying this rule:
(m^6 / m^-7) = m^(6 - (-7)) = m^13
(y^3 / y^-3) = y^(3 - (-3)) = y^6
So, the final simplified expression is:
(5/7) * m^13 * y^6 * r / r^-4
Note: If you need to write the exponents properly, use the caret symbol (^), such as m^13 for m raised to the power of 13, y^6 for y raised to the power of 6, and so on.
To simplify the expression (-10m^(-1)y^(0)r) / (-14m^(-7)y^(-3)r^(-4)), we can use the properties of exponents. Recall that dividing two powers with the same base is equivalent to subtracting their exponents.
Step 1: Simplify the numerator.
The term "y^0" means y raised to the power of zero, which is always equal to 1. Therefore, we can simplify (-10m^(-1)y^(0)r) as (-10m^(-1)r).
Step 2: Simplify the denominator.
The given denominator is -14m^(-7)y^(-3)r^(-4), which means -14m raised to the power of -7, y raised to the power of -3, and r raised to the power of -4.
Step 3: Combine the simplified numerator and denominator.
When dividing, we subtract the exponents. So, (-10m^(-1)r) / (-14m^(-7)y^(-3)r^(-4)) can be rewritten as (-10/(-14)) * (m^(-1-(-7))) * (y^(0-(-3))) * (r^(1-(-4))).
Simplifying further, we have:
(-10/(-14)) * (m^(-1+7)) * (y^(0+3)) * (r^(1+4))
(10/14) * (m^6) * (y^3) * (r^5)
Finally, we can simplify the expression to:
(5/7) * (m^6) * (y^3) * (r^5)
Please note that if any of the variables (m, y, r) have a zero exponent, they will have a value of 1.