Powers - Maths

What does it mean when a number is raised to an exponent?

It indicates how many times the base number is multiplied by itself.

What is the value of 2^7?

128.

How do the powers of ten relate to zeros?

The power indicates the number of zeros following the base number.

What is 10^2?

100, which represents two zeros after the base number 1.

What is the property of any number raised to the power of 1?

It is just itself.

What is the result of 1 raised to any power?

1.

What is the rule for any non-zero number raised to the power of 0?

It equals 1.

How do you simplify when multiplying powers?

You add the exponents.

How do you simplify when dividing powers?

You subtract the exponents.

What is the result of (3^2)^3?

3^6 = 729.

How do you handle powers with fractions?

Apply the power to both the numerator and the denominator.

If a = 5^9 and b = 5^4 × 5^2, what is a/b?

125, because a/b simplifies to 5^3.

What does a negative exponent indicate?

The base is in the denominator, e.g. 5^{-n} = 1/5^{n}.

How can 10,000 be expressed as a power of ten?

10^4.

What do you get when you simplify 4^2 x 4^3?

4^5.

What is the value of 6^3 x 6^5 / 6^6 without a calculator?

36.

What is the result of 2^{-4}?

1/16.