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Q:

# How do you add exponents?

A:

An exponent is a shorthand way of showing how many times to multiply a number by itself. The number 9 with a small raised 3 on its upper right, also commonly expressed as 9^3, represents the base of 9 to the 3rd power, for instance; the raised 3 is the exponent. Simplify multiplication of two exponents with the same base number using exponent addition.

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1. ### Recognize the common base number

In some math expressions, the base numbers are given. In the formula 9^3 times 9^5, for instance, the base number is 9 in each case. In algebraic expressions, the formula might show x^3 times x^5.

2. ### Add exponent numbers and combine the bases

To multiply two like base numbers, add the exponents and merge them into one. In 9^3 times 9^5, adding the exponents 3 and 5 equals 8. Therefore, this two-part formula is simplified to 9^8.

3. ### Solve the equation

Use the simplified base number and exponent to solve the equation. If the objective was to solve for x when you multiply 9^3 times 9^5, 9^8 = x. Multiply 9 by itself, then multiply the result by 9 six more times, or use a scientific calculator and enter 9, the "x to the y power" key and 8.

## Related Questions

• A:

Moving a variable with a negative exponent to the opposite side of the fraction bar and changing the sign of the exponent to positive eliminates the negative exponents, allowing simplification of the fraction as normal. The negative exponent indicates the reciprocal of the term to the positive power.

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• A:

When multiplying or dividing different bases with the same exponent, combine the bases, and keep the exponent the same. For example, X raised to the third power times Y raised to the third power becomes the product of X times Y raised to the third power. When adding or subtracting different bases with the same power, evaluate the exponents first, and then perform the summation.

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• A:

The basic rule in adding and subtracting variables with exponents is they must be like terms. Like terms consist of the same variable or set of variables raised to the same power. The numerical coefficients of these terms may vary, and these are the elements that undergo the addition or subtraction process. The algebraic expressions 2x, 7x and x are like terms, as well as, 4ab^2 and 21ab^2.