Answer :
To evaluate the expression [tex]125^{2/3} + 243^{2/5} - (-5) \times (-7)[/tex], we will solve it step-by-step.
Evaluate [tex]125^{2/3}[/tex]:
- [tex]125[/tex] is [tex]5^3[/tex] because [tex]5 \times 5 \times 5 = 125[/tex].
- Therefore, [tex]125^{2/3} = (5^3)^{2/3} = 5^{(3 \times 2/3)} = 5^2 = 25[/tex].
Evaluate [tex]243^{2/5}[/tex]:
- [tex]243[/tex] is [tex]3^5[/tex] because [tex]3 \times 3 \times 3 \times 3 \times 3 = 243[/tex].
- Therefore, [tex]243^{2/5} = (3^5)^{2/5} = 3^{(5 \times 2/5)} = 3^2 = 9[/tex].
Evaluate [tex]-(-5) \times (-7)[/tex]:
- The expression [tex](-5) \times (-7)[/tex] equals 35 because the product of two negative numbers is positive.
Combine all parts together:
- First, calculate [tex]125^{2/3} + 243^{2/5} = 25 + 9 = 34[/tex].
- Then, calculate [tex]34 - 35 = -1[/tex].
Therefore, the value of the expression is -1.
The correct answer is option B: -1.
