Simplifying Algebraic Expressions 2 Sample Problems

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Here are some tips for Simplifying Algebraic Expressions 2, which aligns with New York state standards:

Simplifying Algebraic Expressions 2

To do well in this topic, you need to know exponents.
To review basic exponents, see here.
To review the Multiplying and Dividing Exponent Expressions topic, see here.

Example 1: Multiplying

Simplify the following. Expand to the form ab^c where a and c are numeric and b is a variable name.
-8n^-3 × 4n^-5

-8n^-3 × 4n^-5 = -8n^-3 × 4n^-5

= -32n^{( ^-3 + ^-5 )}

= -32n^{^-8}

The answer is

Example 2: Exponents

Simplify the following. Expand to the form ab^c where a and c are numeric and b is a variable name.
(-5f^{^-3})²
(-5f^{^-3})² = (-5)²(f^{^-3})² = 25f^{^-6}
The answer is

Example 3: Square Roots

Simplify the following. Expand to the form ab^c where a and c are numeric and b is a variable name.

81f ¹⁰

81f ¹⁰ = 81 ⋅ f ¹⁰ = 9 ² ⋅ (f ⁵)² = 9f ⁵

The answer is

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-8n^-3 × 4n^-5	=	-8n^-3 × 4n^-5
	=	-32n^{( ^-3 + ^-5 )}
	=	-32n^{^-8}