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Simplify the following expressions involving exponents: 1) 20100 ext / 20100, 2) racx32x3, 3) (-2xyz)0, 4) rac(2a5b3)3 (2a2b4)232a19b17
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Step-by-step solution
13 stepsHere are the solutions to the problems.
1) Simplify .
Apply the division rule for exponents, .
Simplify the exponent.
Apply the rule for any non-zero base .
The simplified expression is .
2) Simplify .
Separate the coefficient and variable terms.
Simplify the variable term using the rule .
Multiply the simplified parts.
The simplified expression is .
3) Simplify .
Apply the rule for any non-zero base .
Since the entire expression is raised to the power of 0, the result is 1.
The simplified expression is .
4) Simplify .
Simplify the first term in the numerator, .
Apply and .
Simplify the second term in the numerator, .
Apply and .
Multiply the simplified terms in the numerator.
Apply .
Substitute the simplified numerator back into the original expression.
Simplify the entire fraction.
Since the numerator and denominator are identical, the expression simplifies to 1.
The simplified expression is .
5) Simplify .
Apply the rule for any non-zero base .
Since the entire fraction inside the parentheses is raised to the power of 0, the result is 1.
The simplified expression is .
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