# Simplify (5^(3/2)a^(9/8)b^(-3/4)c^(1/8))^(4/3)

(532a98b-34c18)43
Rewrite the expression using the negative exponent rule b-n=1bn.
(532a981b34c18)43
Multiply 532a981b34.
Combine 532 and 1b34.
(a98532b34c18)43
Combine a98 and 532b34.
(a98⋅532b34c18)43
(a98⋅532b34c18)43
Combine a98⋅532b34 and c18.
(a98⋅532c18b34)43
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to a98⋅532c18b34.
(a98⋅532c18)43(b34)43
Apply the product rule to a98⋅532c18.
(a98⋅532)43(c18)43(b34)43
Apply the product rule to a98⋅532.
(a98)43⋅(532)43(c18)43(b34)43
(a98)43⋅(532)43(c18)43(b34)43
Simplify the numerator.
Multiply the exponents in (a98)43.
Apply the power rule and multiply exponents, (am)n=amn.
a98⋅43⋅(532)43(c18)43(b34)43
Cancel the common factor of 3.
Factor 3 out of 9.
a3(3)8⋅43⋅(532)43(c18)43(b34)43
Cancel the common factor.
a3⋅38⋅43⋅(532)43(c18)43(b34)43
Rewrite the expression.
a38⋅4⋅(532)43(c18)43(b34)43
a38⋅4⋅(532)43(c18)43(b34)43
Cancel the common factor of 4.
Factor 4 out of 8.
a34(2)⋅4⋅(532)43(c18)43(b34)43
Cancel the common factor.
a34⋅2⋅4⋅(532)43(c18)43(b34)43
Rewrite the expression.
a32⋅(532)43(c18)43(b34)43
a32⋅(532)43(c18)43(b34)43
a32⋅(532)43(c18)43(b34)43
Multiply the exponents in (532)43.
Apply the power rule and multiply exponents, (am)n=amn.
a32⋅532⋅43(c18)43(b34)43
Cancel the common factor of 3.
Cancel the common factor.
a32⋅532⋅43(c18)43(b34)43
Rewrite the expression.
a32⋅512⋅4(c18)43(b34)43
a32⋅512⋅4(c18)43(b34)43
Cancel the common factor of 2.
Factor 2 out of 4.
a32⋅512⋅(2(2))(c18)43(b34)43
Cancel the common factor.
a32⋅512⋅(2⋅2)(c18)43(b34)43
Rewrite the expression.
a32⋅52(c18)43(b34)43
a32⋅52(c18)43(b34)43
a32⋅52(c18)43(b34)43
Raise 5 to the power of 2.
a32⋅25(c18)43(b34)43
Multiply the exponents in (c18)43.
Apply the power rule and multiply exponents, (am)n=amn.
a32⋅25c18⋅43(b34)43
Cancel the common factor of 4.
Factor 4 out of 8.
a32⋅25c14(2)⋅43(b34)43
Cancel the common factor.
a32⋅25c14⋅2⋅43(b34)43
Rewrite the expression.
a32⋅25c12⋅13(b34)43
a32⋅25c12⋅13(b34)43
Multiply 12 and 13.
a32⋅25c12⋅3(b34)43
Multiply 2 by 3.
a32⋅25c16(b34)43
a32⋅25c16(b34)43
a32⋅25c16(b34)43
Simplify the denominator.
Multiply the exponents in (b34)43.
Apply the power rule and multiply exponents, (am)n=amn.
a32⋅25c16b34⋅43
Cancel the common factor of 3.
Cancel the common factor.
a32⋅25c16b34⋅43
Rewrite the expression.
a32⋅25c16b14⋅4
a32⋅25c16b14⋅4
Cancel the common factor of 4.
Cancel the common factor.
a32⋅25c16b14⋅4
Rewrite the expression.
a32⋅25c16b1
a32⋅25c16b1
a32⋅25c16b1
Simplify.
a32⋅25c16b
a32⋅25c16b
Move 25 to the left of a32.
25a32c16b
Simplify (5^(3/2)a^(9/8)b^(-3/4)c^(1/8))^(4/3)

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