Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers. a) r^{^1/_6} r^{^5/_6} b) a^{^3/_5} a^{^3/_{10}}

aflacatn 2021-02-22 Answered
Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
a) r1/6 r5/6
b) a3/5 a3/10
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Expert Answer

Jaylen Fountain
Answered 2021-02-23 Author has 170 answers

a) amn=(an)m=amn
The exponent m/n consists of two parts:
The denominator n is the root and the numerator m is the export
Exponent Rule:
am/n=1am/n
Calculation:
r16  r56=r
Apply exponent rule simplify the expression,
r16  r56=r16 + 56
=r66
r16  r56=r
Final statement (a):
r16  r56=r
b) amn=(an)m=amn
The exponent m//n consists of two parts:
The denominator n is the root and the numerator m is the export
Exponent Rule:
am/n=1am/n
Calculation:
a3/5 a3/10
Apply exponent rule in a3/5 a3/10 we get,
a35 a310=a35 + 310
=a3 × 25 × 2 + 310
a610 + 310
a35  a310=a910
Final statement (b):
a35  a310=a910

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