Powers, Exponents, and Roots

Estimate the square root.

• 9

• 10

• 11

• 12

In between what two integers is the square root of 77?

• 5 and 6

• 6 and 7

• 7 and 8

• 8 and 9

Estimate the square root.

• 1

• 2

• 3

• 4

Hey there! Imagine Liam and Aiden are on a math adventure, and they stumble upon a mysterious gate. The gate has a riddle that goes like this: 'What is the Product of Powers Property?' Can you help them unlock the gate?

• Product of Roots Property states that when multiplying two roots with the same base, you multiply the exponents.

• Product of Quotients Property states that when multiplying two quotients with the same base, you subtract the exponents.

• Product of Powers Property states that when multiplying two powers with the same base, you add the exponents.

• Product of Sums Property states that when multiplying two sums with the same base, you add the exponents.

How do you simplify the expression 5^3 * 5^4?

• 5^7

• 5^12

• 5^2

• 5^35

Imagine Aria, Olivia, and Nora are on a treasure hunt. They find a magical door with a puzzle that reads: Simplify the expression (2^5) / (2^3) to unlock the treasure. Can you help them solve it?

• 10

• 8

• 4

• 6

Imagine Henry and Abigail are on a space adventure, exploring the vast universe. They encounter a situation where they need to multiply numbers in scientific notation to calculate the distance between two stars. What should they do with the exponents?

• Add the exponents

• Multiply the exponents

• Subtract the exponents

• Divide the exponents

Imagine Michael, Ethan, and Luna are on a space adventure, exploring the vast universe. They come across a planet that is exactly 3,000,000 miles away from their current location. Help them convert this distance to scientific notation to make navigation easier!

• 3 x 10^6

• 3 x 10^7

• 3 x 10^5

• 3 x 10^8

Hey there, space explorers! 🚀 Imagine Liam, Nora, and Harper are on a mission to a tiny planet called Microscopia. They discovered an element that weighs just 0.000045 grams. Can you help them convert this weight to scientific notation to report back to Earth?

• 4.5 x 10^-4

• 4.5 x 10^5

• 4.5 x 10^-5

• 4.5 x 10^4

Imagine Mason and Nora are on a space adventure, discovering new planets. They need to multiply huge numbers to calculate the distance between planets in scientific notation. How should they do it?

• Divide the coefficients and subtract the exponents.

• Multiply the coefficients and add the exponents.

• Ignore the exponents and multiply the coefficients only.

• Add the coefficients and multiply the exponents.