  Master the 7 pillars of school success

​Simplify:

Multiply the coefficients.
2x5 =10

Next, add exponents of like bases.

Bring down the y^3

Multiplying Exponents
Multiplying Negative Exponents
Multiplying Fractions with Exponents
Multiplying Terms with Fractional Exponents
Multiplying negative exponents

Simplify:

When the bases are the same add the exponents, remember your sign number rules!

When the bases are different, you can’t combine exponents. Leave the terms!

Multiplying terms with fractional exponents

Simplify: x^(1/2)*x^(3/5)

When the bases are the same add the exponent (remember to find common denominators)

x^(1/2)*x^(3/5)
x^ (1/2 + 3/5)
x^ (5/10 + 6/10) = x^ (11/10)

When the bases and exponents are different, you cannot combine.

x^(3/4)*y^(4/5)

Multiplying fractions with exponents

Simplify:
(1/2 )^3* (1/2 )^2

If the bases are the same add the exponents
(1/2 )^3* (1/2 )^2 = ( 1/2 )^5

When the bases are different, but the exponents are the same,group the bases together, and the exponent remains unchanged.

(1/2 )^3 *(3/4 )^3

(1/2 )^3*(3/4 )^3 = (3/8 )^3

When both your bases, and exponents are different, then evaluate each term first, then multiply together.

(2/3)^2 * (3/4)^3
(4/9) * (27/64) = (4*27/9x64) =(3/16)     When an exponent expression is raised to a power, multiply the exponent and the power together.

Do NOT "distribute" Exponents over addition. Use the order of operations, and add, then raise to the power.
For example: (4 + 2)^3 is NOT 4^3 + 2^3, but rather (4 + 2)^3 IS (6)^3.

When multiplying exponents terms with coefficients, multiply the coefficient, and add the exponents with the same bases.

When multiplying exponents by 0 or raising an exponent to the 0 power, the answer is always 1!

(9x^3y^5)0= 1

When multiplying exponent’s terms inside parentheses, you add the exponents because the operation is multiplication.

(a^4*a^5*a^2) = (a^11) Common Core Standard: 8.EE.A.1 ​What are the rules for multiplying exponents?

Multiplying exponents with the same base.
If the bases are the same, then you can simply add the exponents.

​X *   X =X          or y * y = Y

Multiplying exponents with different bases.

If the bases are different, you can not multiply exponents.
For example,

x^3 *y^4 =  You cannot combine because of the different bases.

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5

# Multiplying Exponents

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### Applying the rules for multiplying exponents 