In Exercises 93–102, factor and simplify each algebraic expression. (x+3)^1/2−(x+3)^3/2

In Exercises 93–102, factor and simplify each algebraic expression. (x+5)^−1/2−(x+5)^−3/2

In Exercises 91–100, simplify using properties of exponents. (3y^1/4)³/y^1/12

In Exercises 97–102, write each algebraic expression without parentheses. 1/3(3x)+[(4y)+(−4y)]

Factor completely, or state that the polynomial is prime. 3x^4-12x^2

Simplify by reducing the index of the radical. $\sqrt[4]{7^2}$

Factor and simplify each algebraic expression. $-8(4x + 3)^{-2} + 10(5x + 1)(4x + 3)^{-1}$

In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. |−20| □ |−50|

Perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 282,000,000,000/0.00141

In Exercises 103–114, factor completely. 6x⁴+35x²−6

Factor and simplify each algebraic expression. $16x^{-\frac{3}{4}}+32x^{\frac{1}{4}}$

Perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (66,000×0.001)/(0.003×0.002)

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $\frac{(x^{-2} y)^{-3}}{(x^{2} y^{-1})^{3}}$

Insert either <, >, or = in the shaded area to make a true statement. $\frac{30}{40} - \frac{3}{4} \ \square \ \frac{14}{15} \cdot \frac{15}{14}$

Simplify by reducing the index of the radical. $\sqrt[9]{x^6{y}^3}$

Simplify by reducing the index of the radical. $\sqrt[12]{x^4{y}^8}$

Factor and simplify each algebraic expression.$[12x^{-\frac{1}{2}}+6x^{-\frac{3}{2}}]$

Simplify each rational expression. Also, list all numbers that must be excluded from the domain. [x^3+2x^2]/[x+2]

In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. 8/13÷8/13 □ |−1|

In Exercises 103–114, factor completely. x⁴−5x²y²+4y⁴

In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (3x−4 y z−7)(3x)−3

In Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (49x−2y⁴)^−1/2(xy^1/2)

In Exercises 103–114, factor completely. (x+y)⁴−100(x+y)²

In Exercises 111–120, use the order of operations to simplify each expression. 10²−100÷5²⋅2−3

Multiply or divide as indicated. [(x^2+6x+9)(x+3)]/[(x^2-4)(x-2)]

In Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (x^−5/4y^1/3x^−3/4)⁻⁶

Multiply or divide as indicated. [(x^2-5x-24)/(x^2-x-12)]/[(x^2-10x+16)/(x^2+x-6)]

In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (2^−1x^−3y^−1)^−2(2x^−6y^4)^−2(9x^3y^−3)^0/(2x^−4y^−6)^2