Understanding Rational Exponents and Geometry Applications

What is the first step in solving an equation of the form u^N = D?

• Add N to both sides

• Multiply both sides by N

• Take the nth root of both sides

• Subtract N from both sides

If you have x^5 = 32, what is the value of x?

• 2

• 4

• 8

• 16

When solving x^3 = 8, what operation should be performed to isolate x?

• Multiply both sides by 3

• Take the cube root of both sides

• Square both sides

• Subtract 3 from both sides

Why must you consider both positive and negative solutions when dealing with even powers?

• Even powers always result in negative numbers

• Even powers can have extraneous solutions

• Even powers can result in both positive and negative roots

• Even powers are always positive

What is the fourth root of 256?

• 16

• 8

• 4

• 2

In the formula for the volume of a sphere, V = 4/3 πr^3, what is the first step to isolate r?

• Add 4/3 to both sides

• Multiply both sides by 3/4

• Divide both sides by π

• Subtract π from both sides

How do you find the radius of a cylinder given its volume and height?

• Subtract the height from the volume, then divide by π

• Add the volume and height, then divide by π

• Multiply the volume by the height and π, then take the square root

• Divide the volume by the height and π, then take the square root

What is the cube root of 51.57 rounded to two decimal places?

• 3.72

• 4.12

• 5.67

• 6.89

If the volume of a sphere is 70, what is the first step to find the radius?

• Divide by 4/3

• Multiply by 4/3

• Multiply by π

• Divide by π

What is the final step in finding the radius of a cylinder after dividing the volume by 10π?

• Subtract 10 from both sides

• Take the square root

• Add 10 to both sides

• Multiply by 10