Simplify y to the negative seventh power over x to the negative third power.
a) x ^3 y ^7
b) 1 over quantity x times y to the fourth power end quantity
c) x cubed over y to the seventh power
d) (xy) ^−10
The simplified expression is a) x^3 y^7.
Which expression is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power?
a) y raised to the eighteenth power over z raised to the eighteenth power
b) z raised to the eighteenth power over y raised to the eighteenth power
c) y raised to the ninth power over z raised to the ninth power
d) z raised to the ninth power over y raised to the ninth power
To simplify the given expression, we can use the properties of exponents. When we raise a power to a negative exponent, it becomes the reciprocal of the positive exponent.
So, starting with the expression:
(y^-3 * z^5) / (z^-4 * y^6)^-2
Using the reciprocal property, we get:
(y^6 * z^-4) ^2 / (y^-3 * z^5)^2
Simplifying further, we get:
(y^12 * z^-8) / (y^-6 * z^10)
By multiplying the numerators and denominators, we get:
y^(12-(-6)) * z^(-8-10)
Simplifying the exponents, we get:
y^18 * z^-18
Finally, using the reciprocal property again, we get:
z^18 / y^18
So, the equivalent expression is b) z raised to the eighteenth power over y raised to the eighteenth power.
Simplify m ^7 m ^−4.
a) m ^3
b) one over m cubed
c) −m ^11
d) one over m to the twenty eighth power
To simplify the expression m^7 * m^−4, we can use the property of exponents that states: m^a * m^b = m^(a+b).
So, applying this property, we have:
m^7 * m^−4 = m^(7 + −4)
Simplifying the exponent, we have:
m^(7 + −4) = m^3
Therefore, the simplified expression is a) m^3.
Which expression is equivalent to (4x ^−3 y ^4) ^−2?
a) negative quantity 16 times x raised to the sixth power end quantity over y raised to the eighth power
b) −16x ^6 y ^8
c) 1 over quantity 16 times x raised to the sixth power times y raised to the eighth power end quantity
d) x raised to the sixth power over quantity 16 times y raised to the eighth power end quantity
To simplify the given expression, we use the property of exponents that states: (a^b)^c = a^(b*c).
Starting with (4x^−3y^4)^−2, we can simplify as follows:
(4x^−3y^4)^−2 = 4^−2 * (x^−3)^−2 * (y^4)^−2
Using the property stated above, we have:
4^−2 * (x^−3)^−2 * (y^4)^−2 = 4^−2 * x^(−3*-2) * y^(4*-2)
Simplifying the exponents, we get:
4^−2 * x^6 * y^−8
Remember that 4^−2 is the same as 1/4^2, which equals 1/16. Additionally, y^−8 is the same as 1/y^8.
So, we have:
1/16 * x^6 * (1/y^8) = x^6/y^8 * 1/16
Therefore, the equivalent expression is c) 1 over quantity 16 times x raised to the sixth power times y raised to the eighth power end quantity.
Which is an equivalent expression for 4 times d raised to the negative fifth power all over quantity 18 times d raised to the ninth power end quantity?
a) 0.2d ^14
b) negative 2 over quantity 9 times d raised to the fourth power end quantity
c) 72 over d raised to the fourteenth power
d) 2 over quantity 9 times d raised to the fourteenth power end quantity
To find the equivalent expression, we can simplify the given expression by using the properties of exponents and basic fraction operations.
The expression is:
4 * d^(-5) / (18 * d^9)
First, let's simplify the numerator by applying the property of negative exponents, where d^(-n) is equal to 1 / d^n:
4 * 1 / d^5 = 4/d^5
Next, let's simplify the denominator by applying the property of multiplying exponents when dividing terms with the same base:
18 * d^9 = 18 * 1 / d^(-9) = 18/d^9
Now, let's substitute the simplified numerator and denominator back into the original expression:
(4/d^5) / (18/d^9)
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:
(4/d^5) * (d^9/18)
Simplifying, we have:
4d^9 / 18d^5
To simplify further, we can divide both the numerator and the denominator by the greatest common factor (GCF), which is 2d^5:
(2d^4 * d^5) / (9)
Combining the terms in the numerator, we get:
2d^9 / 9
Therefore, the equivalent expression is c) 72 / d^14.
Simplify (c3)−4.
a) 1 over c raised to the twelfth power
b) 1 over c
c) −c ^12
d) c