Evaluate ((8^2*7^(1/3))/(14^2))^3

Math
(82⋅713142)3
Evaluate the exponents.
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Raise 8 to the power of 2.
(64⋅713142)3
Raise 14 to the power of 2.
(64⋅713196)3
(64⋅713196)3
Factor 4 out of 64⋅713.
(4(16⋅713)196)3
Cancel the common factors.
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Factor 4 out of 196.
(4(16⋅713)4(49))3
Cancel the common factor.
(4(16⋅713)4⋅49)3
Rewrite the expression.
(16⋅71349)3
(16⋅71349)3
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to 16⋅71349.
(16⋅713)3493
Apply the product rule to 16⋅713.
163⋅(713)3493
163⋅(713)3493
Simplify the numerator.
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Raise 16 to the power of 3.
4096(713)3493
Multiply the exponents in (713)3.
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Apply the power rule and multiply exponents, (am)n=amn.
4096⋅713⋅3493
Cancel the common factor of 3.
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Cancel the common factor.
4096⋅713⋅3493
Rewrite the expression.
4096⋅71493
4096⋅71493
4096⋅71493
Evaluate the exponent.
4096⋅7493
4096⋅7493
Reduce the expression by cancelling the common factors.
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Raise 49 to the power of 3.
4096⋅7117649
Multiply 4096 by 7.
28672117649
Cancel the common factor of 28672 and 117649.
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Factor 7 out of 28672.
7(4096)117649
Cancel the common factors.
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Factor 7 out of 117649.
7⋅40967⋅16807
Cancel the common factor.
7⋅40967⋅16807
Rewrite the expression.
409616807
409616807
409616807
409616807
The result can be shown in multiple forms.
Exact Form:
409616807
Decimal Form:
0.24370797…
Evaluate ((8^2*7^(1/3))/(14^2))^3

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