Math.8.EE.1 8.EE.A.1 MA.8.NSO.1.3 Math.8.EE.2 8.EE.A.2 CC.2.2.8.B.1 MA.8.AR.1.1 M08.B-E.1.1.1 M08.B-E.1.1.2

Common Core Standards Exponents
Grade:	8th Grade
Standard:	Math.8.EE.1 or 8.EE.A.1
Description:	Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3^–5 = 3^–3 = 1/3³ = 1/27
Standard:	MA.8.NSO.1.3
Description:	Extend previous understanding of the Laws of Exponents to include integer exponents. Apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions, limited to integer exponents and rational number bases, with procedural fluency.
Standard:	Math.8.EE.2 or 8.EE.A.2
Description:	Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Standard:	CC.2.2.8.B.1
Description:	Apply concepts of radicals and integer exponents to generate equivalent expressions.
Standard:	MA.8.AR.1.1
Description:	Apply the Laws of Exponents to generate equivalent algebraic expressions, limited to integer exponents and monomial bases.
Standard:	M08.B-E.1.1.1
Description:	Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator (with final answers expressed in exponential form with positive exponents).
Standard:	M08.B-E.1.1.2
Description:	Use square root and cube root symbols to represent solutions to equations of the form x2= p and x3= p, where p is a positive rational number. Evaluate square roots of perfect squares (up toand including 122) and cube roots of perfect cubes (up to and including 53) without a calculator.

The product of two terms with exponents and the same base
is equal to the base raised to the sum of the exponents.

\begin{array}{rcl} x^{m} x^{n} & = & x^{(m + n)} \\ 2^{3} 2^{4} & = & 2^{(3 + 4)} \\ = & 2^{7} \end{array}

The quotient of two terms with exponents and the same base
is equal to the base raised to the difference of the exponents.

\begin{array}{rcl} x^{m} \div x^{n} & = & x^{(m - n)} \\ 2^{4} \div 2^{3} & = & 2^{(4 - 3)} \\ = & 2^{1} \end{array}

A term with an exponent raised to a power is equal
to the base raised to the product of the exponents.

\begin{array}{rcl} {(x^{m})}^{n} & = & x^{(m \times n)} \\ {(2^{3})}^{4} & = & 2^{(3 \times 4)} \\ = & 2^{12} \end{array}

A term with a negative exponent is equal to the reciprocal
of the base raised to the opposite of the exponent.

\begin{array}{rcl} x^{- m} & = & \frac{1}{x^{m}} \\ 2^{- 3} & = & \frac{1}{2^{3}} \end{array}

Common Core Standards

Exponents

Math.8.EE.1 or 8.EE.A.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

MA.8.NSO.1.3

Extend previous understanding of the Laws of Exponents to include integer exponents. Apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions, limited to integer exponents and rational number bases, with procedural fluency.

Math.8.EE.2 or 8.EE.A.2

Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

CC.2.2.8.B.1

Apply concepts of radicals and integer exponents to generate equivalent expressions.

MA.8.AR.1.1

Apply the Laws of Exponents to generate equivalent algebraic expressions, limited to integer exponents and monomial bases.

M08.B-E.1.1.1

Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator (with final answers expressed in exponential form with positive exponents).

M08.B-E.1.1.2

Use square root and cube root symbols to represent solutions to equations of the form x2= p and x3= p, where p is a positive rational number. Evaluate square roots of perfect squares (up toand including 122) and cube roots of perfect cubes (up to and including 53) without a calculator.

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