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# Exponents Study Guide: GED Math (page 4)

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Updated on Mar 23, 2011

### Laws of Exponents

When working with exponents, there are three rules that can be helpful.

1. When you multiply powers with the same base, keep the base and add the exponents: 42 × 43 = 42 + 3 = 45.
2. When you divide powers with the same base, keep the base and subtract the exponents: 37 ÷ 34 = 37 – 4 = 33.
3. When you raise a power to a power, you keep the base and multiply the exponents: (73)2 = 73 × 2 = 76.

If two powers are being multiplied together and the bases are not the same, check to see if you can convert the numbers to have the same base to use the preceding laws. For example, to simplify 272 × 32, recognize that 27 can be written as 33. Change the problem to (33)2 × 32. Use law number 3 to get 33 × 2 × 32 = 36 × 32. Now, you can use law number 1 to get 36 + 2 = 38.

### Exponents and the Order of Operations

Be aware of some distinctions when working with the order of operations and exponents. Exponents are done after parentheses and before any other operations, including the negative sign. For example, –32 = –(3 × 3) = –9 because you first take the second power of 3 and then the answer is negative. However, (–3)2 = –3 × –3 = 9, because –3 is enclosed in parentheses.

Example

–20 + (–2 + 5)3 ÷ (10 – 7) × 2 =

Evaluate the parentheses, left to right:

–20 + 33 ÷ 3 × 2.

Now, evaluate the exponent: –20 + 27 ÷ 3 × 2.

Division will be done next: –20 + 9 × 2.

Evaluate multiplication: –20 + 18.

Practice problems for these concepts can be found at:

Exponents and Roots Practice Problems: GED Math