# Evaluate (125/8)^(-2/3)+(81/64)^(-3/2)

(1258)-23+(8164)-32
Simplify each term.
Change the sign of the exponent by rewriting the base as its reciprocal.
(8125)23+(8164)-32
Apply the product rule to 8125.
82312523+(8164)-32
Simplify the numerator.
Rewrite 8 as 23.
(23)2312523+(8164)-32
Apply the power rule and multiply exponents, (am)n=amn.
23(23)12523+(8164)-32
Cancel the common factor of 3.
Cancel the common factor.
23(23)12523+(8164)-32
Rewrite the expression.
2212523+(8164)-32
2212523+(8164)-32
Raise 2 to the power of 2.
412523+(8164)-32
412523+(8164)-32
Simplify the denominator.
Rewrite 125 as 53.
4(53)23+(8164)-32
Apply the power rule and multiply exponents, (am)n=amn.
453(23)+(8164)-32
Cancel the common factor of 3.
Cancel the common factor.
453(23)+(8164)-32
Rewrite the expression.
452+(8164)-32
452+(8164)-32
Raise 5 to the power of 2.
425+(8164)-32
425+(8164)-32
Change the sign of the exponent by rewriting the base as its reciprocal.
425+(6481)32
Apply the product rule to 6481.
425+64328132
Simplify the numerator.
Rewrite 64 as 82.
425+(82)328132
Apply the power rule and multiply exponents, (am)n=amn.
425+82(32)8132
Cancel the common factor of 2.
Cancel the common factor.
425+82(32)8132
Rewrite the expression.
425+838132
425+838132
Raise 8 to the power of 3.
425+5128132
425+5128132
Simplify the denominator.
Rewrite 81 as 92.
425+512(92)32
Apply the power rule and multiply exponents, (am)n=amn.
425+51292(32)
Cancel the common factor of 2.
Cancel the common factor.
425+51292(32)
Rewrite the expression.
425+51293
425+51293
Raise 9 to the power of 3.
425+512729
425+512729
425+512729
To write 425 as a fraction with a common denominator, multiply by 729729.
425⋅729729+512729
To write 512729 as a fraction with a common denominator, multiply by 2525.
425⋅729729+512729⋅2525
Write each expression with a common denominator of 18225, by multiplying each by an appropriate factor of 1.
Multiply 425 and 729729.
4⋅72925⋅729+512729⋅2525
Multiply 25 by 729.
4⋅72918225+512729⋅2525
Multiply 512729 and 2525.
4⋅72918225+512⋅25729⋅25
Multiply 729 by 25.
4⋅72918225+512⋅2518225
4⋅72918225+512⋅2518225
Combine the numerators over the common denominator.
4⋅729+512⋅2518225
Simplify the numerator.
Multiply 4 by 729.
2916+512⋅2518225
Multiply 512 by 25.
2916+1280018225
Add 2916 and 12800.
1571618225
1571618225
The result can be shown in multiple forms.
Exact Form:
1571618225
Decimal Form:
0.86233196…
Evaluate (125/8)^(-2/3)+(81/64)^(-3/2)

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