Lesson 1 of 5
Choose the right power rule and preserve nonzero-base conditions.
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Worked example
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Evaluate and . Check: a nonzero base to zero is 1, and the negative first power is .
Big ideas
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When multiplying powers with the same base, . This rule concerns multiplication, not addition of powers.
For , . A zero denominator is still forbidden even if the simplified expression looks defined there.
For integer powers in their valid domains, . A power of a product applies to every factor; a power does not distribute over a sum.
For , and . A negative exponent changes a factor to its reciprocal rather than making its value negative.
Worked example
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Simplify for . Square first to get , divide coefficients and subtract exponents to get . At , both expressions equal 16.
Step-through
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Worked example: combine powers
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The simplified form does not restore .
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The nonzero condition remains.
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Wrong idea: a negative exponent means a negative answer. For example, , which is positive. The minus sign in the exponent asks for a reciprocal.
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Flashcards
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Multiply same bases by adding exponents.
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Simplify .
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Simplify for .
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Simplify .
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Simplify .
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What is when ?
1.
Rewrite for .
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Does equal for every a?
No; the product rule does not apply to addition.
Why preserve restrictions after exponent simplification?
The original expression may divide by zero at an input the result appears to allow.
True or false
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6 questions. One at a time.
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Self-test
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6 questions. One at a time.
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Start here if it helps: I can connect the conditions by...
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