Understand, Explain, and Apply the Properties of Integer Exponents to Generate Equivalent Numerical Expressions

Standard 8.EE.1 – Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27

Vocabulary for this standard: base, exponent, coefficient, negative exponent, the multiplicative property of exponents, the division power of exponents, powers of powers
EngageNY lesson link – This appears in the first module of the EngageNY curriculum as a standalone topic.
Quick thoughts: This is a crucial concept to understand, conceptually understanding that an exponent is a quantity of multiplications and is treated differently from a coefficient.
A base is a number or expression being multiplied in an exponent
An exponent is a number that describes how many times to use the number in a multiplication.
A coefficient is a number used to multiply a variable.
A negative exponent expresses that the base is the denominator of a fraction instead of the numerator
The multiplicative property of exponents says that when you multiply powers with the same base you just have to add the exponents
The division property of exponents says that when you divide powers with the same base you just have to subtract the exponents
The power of a power property says that when you raise an exponent to another power, you just have to multiply the exponents
Vocab
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