# Evaluate (-8/125)^(4/3)

(-8125)43
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to -8125.
(-1)43(8125)43
Apply the product rule to 8125.
(-1)4384312543
(-1)4384312543
Reduce the expression by cancelling the common factors.
Rewrite -1 as (-1)3.
((-1)3)4384312543
Apply the power rule and multiply exponents, (am)n=amn.
(-1)3(43)84312543
Cancel the common factor of 3.
Cancel the common factor.
(-1)3(43)84312543
Rewrite the expression.
(-1)484312543
(-1)484312543
Simplify the expression.
Raise -1 to the power of 4.
184312543
Multiply 84312543 by 1.
84312543
84312543
84312543
Simplify the numerator.
Rewrite 8 as 23.
(23)4312543
Apply the power rule and multiply exponents, (am)n=amn.
23(43)12543
Cancel the common factor of 3.
Cancel the common factor.
23(43)12543
Rewrite the expression.
2412543
2412543
Raise 2 to the power of 4.
1612543
1612543
Simplify the denominator.
Rewrite 125 as 53.
16(53)43
Apply the power rule and multiply exponents, (am)n=amn.
1653(43)
Cancel the common factor of 3.
Cancel the common factor.
1653(43)
Rewrite the expression.
1654
1654
Raise 5 to the power of 4.
16625
16625
The result can be shown in multiple forms.
Exact Form:
16625
Decimal Form:
0.0256
Evaluate (-8/125)^(4/3)

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