## Questions and Answers

What is another name for exponents?

Powers

What does 82 mean?

8 to the power 2

What does x0 equal to?

1

What happens to a number when the exponent is negative?

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Which of the following is NOT one of the Laws of Exponents?

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What is the key to understanding the Laws of Exponents?

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When applying the law (xm)n = xmn, how many times do we end up multiplying 'x'?

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According to the law (xy)n = xnyn, what does (xy)3 equal to?

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What is the result of x2/x2 according to the law xm/xn = xm-n?

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In the law xm/n = n√xm = (n√x )m, what does x(mn) equal to?

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According to the law (x/y)n = xn/yn, what is the result of (x/y)3?

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What is the value of x1/n where n is a positive integer?

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When simplifying x(mn) using the law x(mn) = x(m × 1/n), what is the result?

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## Study Notes

### Exponents

- Exponents are also known as indices or powers.

### Exponent Notation

- The notation 82 means 8 raised to the power of 2, or 8 squared.
- Any number raised to the power of 0 equals 1.

### Negative Exponents

- When a number has a negative exponent, it becomes a reciprocal (i.e., 1 divided by the number).

### Laws of Exponents

- The key to understanding the Laws of Exponents is to recognize that exponents are a shorthand for repeated multiplication.
- One of the Laws of Exponents is not "x^m × x^n = x^(m+n+c)", where c is a constant.

### Power of a Power

- When applying the law (xm)n = xmn, we end up multiplying 'x' mn times.

### Product of Powers

- According to the law (xy)n = xnyn, (xy)3 equals to x3y3.

### Quotient of Powers

- The result of x2/x2 according to the law xm/xn = xm-n is 1 (since 2-2 = 0).

### Power of a Product

- In the law xm/n = n√xm = (n√x)m, x(mn) equals to (n√x)m.
- According to the law (x/y)n = xn/yn, the result of (x/y)3 is x3/y3.

### Fractional Exponents

- The value of x1/n, where n is a positive integer, is the nth root of x.

### Simplifying Exponents

- When simplifying x(mn) using the law x(mn) = x(m × 1/n), the result is x(m/n).

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