How do you factor the difference of powers?

How do you factor the difference of powers?

Factoring a4 – b. We can factor a difference of fourth powers (and higher powers) by treating each term as the square of another base, using the power to a power rule. For example, to factor x4 – y4, we treat x4 as (x2)2 and y4 as (y2)2. Thus, x4 – y4 = (x2)2 – (y2)2 = (x2 + y2)(x2 – y2) = (x2 + y2)(x + y)(x – y).

What are the factors of 144?

Factors of 144

• Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144.
• Negative Factors of 144: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -36, -48, -72 and -144.
• Prime Factors of 144: 2, 3.
• Prime Factorization of 144: 2 × 2 × 2 × 2 × 3 × 3 = 24 × 32
• Sum of Factors of 144: 403.

What are all the factors of 72?

The sum of all factors of 72 is 195.

• Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
• Negative Factors of 72: -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36 and -72.
• Prime Factors of 72: 2, 3.
• Prime Factorization of 72: 2 × 2 × 2 × 3 × 3 = 23 × 32
• Sum of Factors of 72: 195.

Is 4000 a perfect square?

Is the number 4000 a Perfect Square? The prime factorization of 4000 = 25 × 53. Here, the prime factor 2 is not in the pair. Therefore, 4000 is not a perfect square.

What is the rule for adding exponents?

Remember, to add or subtract numbers that have exponents you must first make sure that the base and exponent of the two terms you are trying to add or subtract are the same. If they are the same, then all you have to do is add together their coefficients and keep the base and exponent the same.

What is the rule for subtracting exponents?

Explanation: When two exponents with the same base are being divided, subtract the exponent of the denominator from the exponent of the numerator to yield a new exponent. Attach that exponent to the base, and that is your answer.

What does 10 to the power of 8 mean?

100,000,000
108=100,000,000. (one hundred million) 10-7=0.0000001. (one ten millionth)

Which is the principal nth root of a number?

If a a is a real number with at least one n th root, then the principal nth root of a a is the number with the same sign as a a that, when raised to the n th power, equals a a. The principal n th root of a a is written as n√a a n, where n n is a positive integer greater than or equal to 2.

Can you write radicals as rational exponents of nth roots?

Simplify Nth roots. Write radicals as rational exponents. Although square roots are the most common rational roots, we can also find cube roots, 4th roots, 5th roots, and more. Just as the square root function is the inverse of the squaring function, these roots are the inverse of their respective power functions.

What is the sum and difference of powers?

Sum and difference of powers. The sum and difference of powers are powerful factoring techniques that, respectively, factor a sum or a difference of certain powers.

Can a root be negative with a numerator other than 1?

If the index n n is even, then a a cannot be negative. We can also have rational exponents with numerators other than 1. In these cases, the exponent must be a fraction in lowest terms. We raise the base to a power and take an n th root. The numerator tells us the power and the denominator tells us the root.