Understanding Exponents
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Algebra 2 › Understanding Exponents
Simplify .
Explanation
To solve this expression, remove the outer exponent and expand the terms.
By exponential rules, add all the powers when multiplying like terms.
The answer is:
Expand:
Explanation
When we expand exponents, we simply repeat the base by the exponential value.
Therefore:
Evaluate:
Explanation
When dealing with negative exponents, we write . Therefore
.
Expand
Explanation
When expanding exponents, we repeat the base by the exponential value.
Expand
Explanation
To expand the exponent, we multiply the base by the power it is being raised to.
Solve for :
Explanation
Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation.
Subtract from both sides:
Evaluate:
Explanation
When dealing with exponents, we convert as such: . Therefore,
.
Evaluate:
Explanation
When dealing with negative exponents, we convert to fractions as such: which
is the positive exponent raising base
.
Simplify:
Explanation
When an exponent is negative, we express as such:
is the positive exponent, and
is the base.
.
Evaluate
Explanation
When dealing with fractional exponents, remember this form:
is the index of the radical which is also the denominator of the fraction,
represents the base of the exponent, and
is the power the base is raised to. That value is the numerator of the fraction.