Simplify (−4b)(−19b).
a) 76b
b) −76b
c) 76b2
d) −76b2
(-4b)(-19b) simplifies to 76b^2.
Therefore, the correct answer is c) 76b^2.
Simplify −4r(−11r + 2r − 14).
a) −36r2 + 56r
b) −36r2 − 56r
c) 36r2 + 56
d) 36r2 + 56r
-4r(-11r + 2r - 14) simplifies to 36r^2 + 56r.
Therefore, the correct answer is d) 36r^2 + 56r.
Simplify seven ninths times a times four fifths times a.
a) 56 over 45
b) 28 over 45 times a
c) 28 over 45 times a squared
d) 56 over 45 times a squared
Seven ninths times a times four fifths times a simplifies to:
(7/9) * a * (4/5) * a
= (28/45) * a^2
Therefore, the correct answer is c) 28/45 times a squared.
Simplify 2.5p(2 − 0.5p).
a) 5p − 0.5p2
b) 5p − 1.25p2
c) 5 − 0.5p2
d) 5 − 1.25p2
2.5p(2 - 0.5p) simplifies to:
5p - 1.25p^2
Therefore, the correct answer is b) 5p - 1.25p^2.
Multiply −14y(7y − 5).
a) −98y2 + 70y
b) −98y2 + 70
c) −98y2 − 5
d) 98y2 − 70y
−14y(7y − 5) simplifies to:
-98y^2 + 70y
Therefore, the correct answer is a) −98y^2 + 70y.
Simplify negative two fifths times m times quantity negative four ninths times m minus one seventh end quantity.
a) 8 over 45 times m squared plus one seventh
b) negative 8 over 45 times m squared minus 2 over 35 times m
c) 8 over 45 times m squared plus 2 over 35 times m
d) negative 8 over 45 times m squared plus 2 over 35 times m
Negative two fifths times m times quantity negative four ninths times m minus one seventh end quantity simplifies to:
(-2/5) * m * (-4/9) * m - (-2/5) * m * (1/7)
= (8/45) * m^2 + (2/35) * m
Therefore, the correct answer is c) 8/45 times m squared plus 2/35 times m.
Multiply 3.2x and 4x.
a) 12.8x2
b) 7.2x2
c) 12.8x
d) 7.2x
Multiplying 3.2x and 4x gives us:
3.2x * 4x = 12.8x^2
Therefore, the correct answer is a) 12.8x^2.
Simplify y to the negative eighth power over x to the negative fifth power.
a) (xy)−13
b) x to the fifth power over y to the eighth power
c) x5y8
d) 1 over quantity x times y cubed end quantity
Simplifying y to the negative eighth power over x to the negative fifth power means we move y to the denominator and change its exponent to positive, and move x to the numerator and change its exponent to positive:
y^-8 / x^-5 = x^5 / y^8
Therefore, the correct answer is c) x^5y^8.
Simplify (c2)−3.
a) c
b) −c6
c) 1 over c
d) 1 over c raised to the sixth power
Simplifying (c^2)^-3 means we apply the exponent to both the base and the exponent:
(c^2)^-3 = c^(2*-3)
c^(2*-3) = c^-6
Since a negative exponent indicates the reciprocal of the base raised to the positive exponent, c^-6 can be rewritten as 1/c^6.
Therefore, the correct answer is d) 1 over c raised to the sixth power.
Simplify m8m−6.
a) one over m to the forty eighth power
b) m2
c) one over m squared
d) −m14
To simplify m^8 * m^-6, we can combine the two exponents by adding them:
m^8 * m^-6 = m^(8+(-6)) = m^2
Therefore, the correct answer is b) m^2.
Which expression is equivalent to quantity y raised to the negative second power times z raised to the third power end quantity over quantity z raised to the negative fourth power times y raised to the fifth power end quantity all raised to the negative second power?
a) y raised to the seventh power over z raised to the seventh power
b) z raised to the seventh power over y raised to the seventh power
c) y raised to the fourteenth power over z raised to the fourteenth power
d) z raised to the fourteenth power over y raised to the fourteenth power
To simplify the given expression, we can apply the power of a power rule and the negative exponent rule.
Using the power of a power rule:
(y^-2 * z^3) / (z^-4 * y^5)^-2
= (y^-2 * z^3) / (z^-4 * y^5)^-2
= (y^-2 * z^3) / (z^4 * y^-10)
Now, using the negative exponent rule to move the exponents to the numerator or denominator:
= (z^3 * y^10) / (y^2 * z^4)
Finally, simplifying the expression by combining like terms:
= y^(10-2) / z^(4-3)
= y^8 / z^1
= y^8 / z
Therefore, the correct answer is c) y raised to the fourteenth power over z raised to the fourteenth power.
Which expression is equivalent to (3x−4y5)−2?
a) −9x8y10
b) x raised to the eighth power over quantity 9 times y raised to the tenth power end quantity
c) negative quantity 9 times x raised to the eighth power end quantity over y raised to the tenth power
d) 1 over quantity 9 times x raised to the eighth power times y raised to the tenth power end quantity
To find the expression equivalent to (3x-4y^5)^-2, we need to apply the negative exponent to each term inside the parentheses:
(3x-4y^5)^-2 = 1 / (3x-4y^5)^2
Now, we can simplify the expression inside the parentheses:
(3x-4y^5)^2 = (3x)^2 - 2(3x)(4y^5) + (4y^5)^2
= 9x^2 - 24xy^5 + 16y^10
Taking the reciprocal gives us:
1 / (9x^2 - 24xy^5 + 16y^10)
Therefore, the correct answer is d) 1 over quantity 9 times x raised to the eighth power times y raised to the tenth power end quantity.
Which is an equivalent expression for 6 times d raised to the negative fourth power all over quantity 21 times d raised to the seventh power end quantity?
a) 2 over quantity 7 times d raised to the eleventh power end quantity
b) 126 over d raised to the eleventh power
c) 0.3d11
d) negative 2 over quantity 7 times d raised to the third power end quantity
To find the equivalent expression, we can simplify the given expression by applying the negative exponent and dividing the coefficients:
6(d^-4) / (21(d^7))
= (6 / 21) * (d^-4 / d^7)
= 6/21 * d^(-4-7)
= 2/7 * d^(-11)
Therefore, the correct answer is a) 2 over quantity 7 times d raised to the eleventh power end quantity.
Simplify a raised to the negative fourth power over quantity 2 times b squared end quantity all cubed.
a) 1 over quantity 8 times a raised to the twelfth power times b raised to the sixth power end quantity
b) 1 over quantity 6 times a raised to the twelfth power times b raised to the sixth power end quantity
c) quantity 8 times b raised to the sixth power end quantity over a raised to the twelfth power
d) 8b6a12
To simplify a^(-4) / (2b^2)^3, we need to simplify the exponent and the denominator first:
a^(-4) / (2b^2)^3 = a^(-4) / 8b^6
We can simplify the expression further by applying the negative exponent and dividing the coefficients:
= 1 / (8a^4b^6)
Now, we can rewrite the expression with the constants in the numerator and the variables with their respective exponents in the denominator:
= 1 / (8 * a^4 * b^6)
Therefore, the correct answer is b) 1 over quantity 8 times a raised to the twelfth power times b raised to the sixth power end quantity.